Daily Papers

In recent years, agentic orchestration has been widely applied to solve complex human tasks. However, existing orchestration learning still faces key challenges, including hand-designed curricula, advantage collapse when a task's rollouts all reach the same outcome, and unreliable evaluation signals that judge each skill by one noisy score. To address these challenges, we propose R^2Orch, a new paradigm of Recursive Self-Play Orchestration: an inner loop of self-play that improves the orchestrator on self-chosen tasks, and an outer loop that improves how the inner loop improves. To support this paradigm, we introduce Recursive Learnability, a training objective that rewards a Proposer for choosing tasks whose rollouts keep reaching different outcomes as skills are withdrawn. Built on this objective, we further propose Skill Withdrawal, in which the outer loop withdraws each skill once a controlled evaluation within self-play shows that the orchestrator performs as well without it. Moreover, the two loops form one cycle: failures are distilled into skills, skills into parameters, and withdrawals lead the Proposer to new failures, so the orchestrator moves toward zero-skill deployment. Experimental results on twelve datasets show that R^2Orch consistently outperforms baselines across question answering, math, code, and interactive tasks. Our code is available at https://github.com/beita6969/R2Orch.

AI systems increasingly participate in their own improvement: revising their outputs, adapting their own harnesses during deployment, training on data they generate, and, increasingly, conducting AI research itself. This literature is described under a vocabulary ("self-refine," "self-reward," "self-play," "self-evolve") that conflates fundamentally different ambitions. We survey 1,250 arXiv papers (2024-2026) along two axes: what the system improves -- its behavior in deployment, its policy through training, its evaluator, or the research process itself -- and the degree of loop closure (human-in-the-loop to fully closed). The taxonomy separates bounded self-refinement -- convergent, evaluable, and already industrial practice -- from open-ended recursive self-improvement (RSI), which remains bounded by grounding requirements, collapse dynamics, and compute constraints on every measured axis. Its distinctive feature is a dedicated category for self-evaluation: every improvement loop is a claim that some signal can substitute for human judgment. We survey the evaluator design space -- judges, process reward models, verifiers, rubrics, meta-evaluation -- order the signals into a verification hierarchy from formal verifiers (strongest) to intrinsic self-assessment (weakest), and observe that demonstrated self-improvement strength tracks this hierarchy, that its failure modes (self-confirming loops, model collapse, diversity collapse) follow from its violations, and that the "research direction-setting" bottleneck keeping humans in the loop sits at the top of that hierarchy. We connect the technical literature to the theory of RSI limits and to the safety and governance questions raised by frontier-lab accounts of closing the loop, and identify governance-grade measurement of self-improvement as the field's most underpopulated niche.

Forecasting when AI systems will become capable of meaningfully accelerating AI research is a central challenge for AI safety. Existing benchmarks measure broad capability growth, but may not provide ample early warning signals for recursive self-improvement. We propose measuring AI's capability to autonomously implement end-to-end machine learning pipelines from past AI research breakthroughs, given a minimal task description. By providing a concise task description instead of the full prior work as reference, we hope to better elicit emerging AI research taste. We introduce a proof-of-concept benchmark in which frontier coding agents autonomously implement an AlphaZero-style machine learning pipeline for Connect Four on consumer hardware within a three-hour budget, and we evaluate the resulting game AIs in a round-robin tournament anchored to the Pascal Pons Connect Four solver. Across four agents with eight trials each, we find substantial differentiation: Claude Opus 4.7 won as first-mover against Pons in seven of eight trials, statistically significantly better than the other agents tested, none of which exceeded two of eight. The task, which no frontier agent could reliably complete when we began development in January of 2026, is now near-saturation. Our evaluation also surfaced anomalous behavior in GPT-5.4, which consistently used far less of its allocated time budget than other agents. A follow-up 16-trial probe using shorter, less evaluation-coded prompts substantially increased GPT-5.4's time-budget usage, consistent with but not diagnostic of sandbagging; Bradley-Terry ratings across probe conditions showed only directional differences, despite significant differences in time-budget usage. We release our data, code, and prompts to support reproduction and extension.

Recursive self-improvement (RSI) lets a system improve the model-building machinery from its own failures, so every later model inherits the gain. Yet RSI has been validated almost exclusively on coding and formal benchmarks such as science QA and mathematics. This format bound limits RSI to improvement within a machine-checkable slice, not general capability where questions are open and correctness is settled by argument, replication, or measurement. We argue RSI must next operate across real, diverse scientific, engineering, and meta-scientific domains, not where formal evaluation is merely tractable. To that end we present MetaRSI-v1, where improvement is the scheduled composition of three typed operators over one unified paradigm. Data-RSI amplifies existing competence and marks its boundary; Harness-RSI edits a five-slot scaffold without touching weights; Model-RSI internalizes capability into parameters through bounded training. Sharing one loop kernel and artifact vocabulary, they make data, scaffold, and model changes composable rather than exclusive. A two-axis optimizer jointly decides operator order and each operator's proposal policy, while a meta-level policy revises the schedule across terms. We validate MetaRSI-v1 under the field's standard evaluations, on code and closed-form science, with no external teacher: the target model plays every role in its own loop. MetaRSI-v1 reframes self-improvement from a single-surface edit to a composition across the full model-production pipeline, opening two paths: a model route internalizing capability through training, and a harness route leaving weights untouched and thus extending self-improvement to any model reachable through an interface, with Data-RSI redefined as the shared substrate feeding both. The framework further yields refutable laws on where loops exist, how operators compose, and what supervision buys.

Recent advances in large language models have made automatic game generation increasingly feasible, yet reliably improving generated games beyond a playable version remains challenging. Naive iterative refinement can easily overfit a small set of test cases, producing fragile games with unresolved bugs, missing behaviors, and poor generalization to broader player interactions. We introduce RSIGame, an autonomous agentic game development framework with recursive self-improvement. RSIGame organizes development into complementary local and global loops. Concretely, a local explore-diagnose-improve loop broadly explores the executable game, diagnoses and prioritizes discovered issues, and performs evidence-grounded revision, where an evolving checklist continually accumulates new testing and improvement guidance. A global loop tracks overall quality, preserves the best checkpoint, and detects saturation or regression over long-horizon development. Beyond test-time improvement, RSIGame further internalizes successful development experience into the generator through training. Across 140 GameCraft-Bench tasks, two game engines, and five generators, RSIGame consistently improves game quality under matched development budgets. Notably, experience internalization enables Qwen3.8-27B to reach 61.38 on Godot and 58.53 on Phaser, exceeding GPT-5.5 one-shot scores while reducing Qwen's generation tokens by 11 times.

Harness development plays a crucial role in building capable AI agents. Recent approaches improve harnesses through recursive self-improvement (RSI), but their performance gains often come with higher execution costs. We introduce HarnessPro, a label-free method for evolving harnesses to improve task performance while reducing execution cost. In this setting, candidate harnesses are evaluated using LLM-generated tests without access to ground-truth solutions or official tests. Specialized agents diagnose execution trajectories, plan updates with different performance-cost priorities, and implement them as candidate harnesses. Rather than returning a single harness, HarnessPro uses normalized weighted squared-distance selection to provide cost-focused (lite), balanced (medium), and performance-focused (heavy) harnesses for different deployment budgets. Selected harnesses enter the next iteration, where execution feedback guides further updates. Our experiments cover Terminal-Bench 2, SWE-Bench Pro, and ProgramBench, using GPT-5.5 with Codex and GLM-5.2 with Claude Code. Across these benchmarks using GPT-5.5 with Codex, the heavy mode of HarnessPro achieves an average pass-rate gain of 2.0 percentage points and an average per-task cost reduction of 26.1% relative to RHO. This advantage also holds when using GLM-5.2 with Claude Code. Code is available at https://github.com/pzs19/HarnessPro

Self-play, characterized by agents' interactions with copies or past versions of itself, has recently gained prominence in reinforcement learning. This paper first clarifies the preliminaries of self-play, including the multi-agent reinforcement learning framework and basic game theory concepts. Then it provides a unified framework and classifies existing self-play algorithms within this framework. Moreover, the paper bridges the gap between the algorithms and their practical implications by illustrating the role of self-play in different scenarios. Finally, the survey highlights open challenges and future research directions in self-play. This paper is an essential guide map for understanding the multifaceted landscape of self-play in RL.

LLM self-play algorithms are notable in that, in principle, nothing bounds their learning: a Conjecturer model creates problems for a Solver, and both improve together. However, in practice, existing LLM self-play methods do not scale well with large amounts of compute, instead hitting learning plateaus. We argue this is because over long training runs, the Conjecturer learns to hack its reward, collapsing to artificially complex problems that do not help the Solver improve. To overcome this, we introduce Self-Guided Self-Play (SGS), a self-play algorithm in which the language model itself guides the Conjecturer away from degeneracy. In SGS, the model takes on three roles: Solver, Conjecturer, and a Guide that scores synthetic problems by their relevance to unsolved target problems and how clean and natural they are, providing supervision against Conjecturer collapse. Our core hypothesis is that language models can assess whether a subproblem is useful for achieving a goal. We evaluate the scaling properties of SGS by running training for significantly longer than prior works and by fitting scaling laws to cumulative solve rate curves. Applying SGS to formal theorem proving in Lean4, we find that it surpasses the asymptotic solve rate of our strongest RL baseline in fewer than 80 rounds of self-play and enables a 7B parameter model, after 200 rounds of self-play, to solve more problems than a 671B parameter model pass@4.

Self-play (SP) is a popular multi-agent reinforcement learning (MARL) framework for solving competitive games, where each agent optimizes policy by treating others as part of the environment. Despite the empirical successes, the theoretical properties of SP-based methods are limited to two-player zero-sum games. However, for mixed cooperative-competitive games where agents on the same team need to cooperate with each other, we can show a simple counter-example where SP-based methods cannot converge to a global Nash equilibrium (NE) with high probability. Alternatively, Policy-Space Response Oracles (PSRO) is an iterative framework for learning NE, where the best responses w.r.t. previous policies are learned in each iteration. PSRO can be directly extended to mixed cooperative-competitive settings by jointly learning team best responses with all convergence properties unchanged. However, PSRO requires repeatedly training joint policies from scratch till convergence, which makes it hard to scale to complex games. In this work, we develop a novel algorithm, Fictitious Cross-Play (FXP), which inherits the benefits from both frameworks. FXP simultaneously trains an SP-based main policy and a counter population of best response policies. The main policy is trained by fictitious self-play and cross-play against the counter population, while the counter policies are trained as the best responses to the main policy's past versions. We validate our method in matrix games and show that FXP converges to global NEs while SP methods fail. We also conduct experiments in a gridworld domain, where FXP achieves higher Elo ratings and lower exploitabilities than baselines, and a more challenging football game, where FXP defeats SOTA models with over 94% win rate.

Deep search agents have emerged as a promising paradigm for addressing complex information-seeking tasks, but their training remains challenging due to sparse rewards, weak credit assignment, and limited labeled data. Self-play offers a scalable route to reduce data dependence, but conventional self-play optimizes students only through sparse outcome rewards, leading to low learning efficiency. In this work, we observe that self-play naturally produces a question construction path (QCP) during task generation, an intermediate artifact that captures the reverse solution process. This reveals a new source of privileged information: self-play can provide high-quality privileged information for the self-distillation at low cost and at scale, without relying on human feedback or curated privileged information. Leveraging this insight, we propose Privileged Information Self-Play (π-Play), a novel multi-agent self-evolution framework combining self-play and self-distillation. In π-Play, an examiner generates tasks together with QCPs, and a teacher employs QCP as privileged context to densely supervise a student via self-distillation. This design transforms sparse-reward self-play into a dense-feedback co-evolution. Extensive experiments show that data-free π-Play surpasses fully supervised search agents and improves evolutionary efficiency by 2-3times over conventional self-play. Code is available at https://github.com/zhyaoch/pi-play.

In this paper, we tackle the problem of learning to play 3v3 multi-drone volleyball, a new embodied competitive task that requires both high-level strategic coordination and low-level agile control. The task is turn-based, multi-agent, and physically grounded, posing significant challenges due to its long-horizon dependencies, tight inter-agent coupling, and the underactuated dynamics of quadrotors. To address this, we propose Hierarchical Co-Self-Play (HCSP), a hierarchical reinforcement learning framework that separates centralized high-level strategic decision-making from decentralized low-level motion control. We design a three-stage population-based training pipeline to enable both strategy and skill to emerge from scratch without expert demonstrations: (I) training diverse low-level skills, (II) learning high-level strategy via self-play with fixed low-level skills, and (III) joint fine-tuning through co-self-play. Experiments show that HCSP achieves superior performance, outperforming non-hierarchical self-play and rule-based hierarchical baselines with an average 82.9% win rate and a 71.5% win rate against the two-stage variant. Moreover, co-self-play leads to emergent team behaviors such as role switching and coordinated formations, demonstrating the effectiveness of our hierarchical design and training scheme. The project page is at https://sites.google.com/view/hi-co-self-play.

Large language models (LLMs) have advanced rapidly in recent years, driven by scale, abundant high-quality training data, and reinforcement learning. Yet this progress faces a fundamental bottleneck: the need for ever more data from which models can continue to learn. In this work, we propose a reinforcement learning approach that removes this dependency by enabling models to improve without additional data. Our method leverages a game-theoretic framework of self-play, where a model's capabilities are cast as performance in a competitive game and stronger policies emerge by having the model play against itself - a process we call Language Self-Play (LSP). Experiments with Llama-3.2-3B-Instruct on instruction-following benchmarks show that pretrained models can not only enhance their performance on challenging tasks through self-play alone, but can also do so more effectively than data-driven baselines.

Recent advances in reinforcement learning have shown that language models can develop sophisticated reasoning through training on tasks with verifiable rewards, but these approaches depend on human-curated problem-answer pairs and domain-specific reward engineering. We introduce SPIRAL, a self-play framework where models learn by playing multi-turn, zero-sum games against continuously improving versions of themselves, eliminating the need for human supervision. Through self-play, SPIRAL generates an infinite curriculum of progressively challenging problems as models must constantly adapt to stronger opponents. To enable this self-play training at scale, We implement a fully online, multi-turn, multi-agent reinforcement learning system for LLMs and propose role-conditioned advantage estimation (RAE) to stabilize multi-agent training. Using SPIRAL, self-play on zero-sum games produces reasoning capabilities that transfer broadly. Training Qwen3-4B-Base on Kuhn Poker alone achieves 8.6% improvement on math and 8.4% on general reasoning, outperforming SFT on 25,000 expert game trajectories. Analysis reveals that this transfer occurs through three cognitive patterns: systematic decomposition, expected value calculation, and case-by-case analysis. Multi-game training (TicTacToe, Kuhn Poker, Simple Negotiation) further enhances performance as each game develops distinct reasoning strengths. Applying SPIRAL to a strong reasoning model (DeepSeek-R1-Distill-Qwen-7B) can still lead to 2.0% average improvement. These results demonstrate that zero-sum games naturally develop transferable reasoning capabilities, highlighting a promising direction for autonomous reasoning development.

Self-play is an effective paradigm for language-model self-evolution, but without guidance, solver performance can plateau or decline across rounds. Unguided methods steer question generation with signals such as difficulty, learnability, or diversity. These signals keep questions challenging and varied but do not specify which unresolved reasoning weaknesses later rounds should target. Guided methods obtain direction from external task resources, including human examples, document corpora, or specified difficulty targets, and therefore rely on task information supplied outside the self-play loop. We show that the needed direction can instead be derived from the solver's own failure history. We introduce DiagEvo, whose diagnostician extracts recurring error causes from this history and stores them in a hierarchical error-cause memory. The memory groups related causes under skill nodes and tracks each as Active or Mastered according to self-consistency on targeted questions. The challenger uses these states and recurrence counts to balance cause-targeted generation with free exploration. Double-confidence filtering retains intermediate-difficulty questions only when the most common solver answer has a clear vote lead. DiagEvo derives its curriculum from information produced during self-play, without external task resources. With the default 4B diagnostician, DiagEvo outperforms every baseline in mean accuracy across all nine benchmarks for each of the three solvers: Qwen3-4B, Qwen3-8B, and OctoThinker-8B. On Qwen3-8B, it reaches 72.3% mean accuracy across five mathematical reasoning benchmarks, 4.5 percentage points above R-Zero. Its mean accuracy across all nine benchmarks is 57.4%, 1.1 percentage points above DARC. Ablations show that the hierarchical error-cause memory and double-confidence filtering both contribute to these gains.

Game-playing agents like AlphaGo have achieved superhuman performance through self-play, which is theoretically guaranteed to yield optimal policies in competitive games. However, most language tasks are partially or fully cooperative, so it is an open question whether techniques like self-play can effectively be used to improve language models. We empirically investigate this question in a negotiation game setting known as Deal or No Deal (DoND). Crucially, the objective in DoND can be modified to produce a fully cooperative game, a strictly competitive one, or anything in between. We finetune language models in self-play over multiple rounds of filtered behavior cloning in DoND for each of these objectives. Contrary to expectations, we find that language model self-play leads to significant performance gains in both cooperation and competition with humans, suggesting that self-play and related techniques have promise despite a lack of theoretical guarantees.

Continuous self-improvement requires an ever-expanding pool of self-generated, diverse, adaptive goals. For language agents, existing training environment pools (hand-curated, statically synthesized, or frozen-verifier) keep the goal distribution fixed as the learner scales. We introduce SPADE (Self-Play in Adaptive Synthetic Executable Environments), a self-play RL framework in which a single LLM plays two roles: an Environment Designer that writes complete, long-horizon training environments as executable code with an OpenAI Gym-style reset()/step() interface, and a Reasoning Agent that learns to act in them. Each is a stateful, multi-turn environment (state transitions, reward functions, and verification code), so one interface spans reasoning problems and multi-step agentic tool use. The Reasoning Agent's regret is estimated using the gap between its reward with and without privileged hints; in optimizing this regret signal the Environment Designer learns to target environments at the edge of the agent's capabilities while keeping them feasible. Through extensive experimentation, we find several components critical to success: grounding the Environment Designer on documents sampled from a large pretraining corpus, and giving it an accumulated environment memory. Scaling to 30B-parameter models, SPADE improves over the strongest fixed-environment baseline by +5.3 on average across eight held-out math, science, code, and reasoning benchmarks, and lifts the tool-use setting by +5.7 on BFCL-v4 multi-turn and +13.9 on ACEBench-Agent; on the games setting, the margin over the strongest baseline grows with model scale. By making environment design itself a learnable component, SPADE takes a concrete step toward open-ended self-improvement.

Acquiring a diverse repertoire of general-purpose skills remains an open challenge for robotics. In this work, we propose self-supervising control on top of human teleoperated play data as a way to scale up skill learning. Play has two properties that make it attractive compared to conventional task demonstrations. Play is cheap, as it can be collected in large quantities quickly without task segmenting, labeling, or resetting to an initial state. Play is naturally rich, covering ~4x more interaction space than task demonstrations for the same amount of collection time. To learn control from play, we introduce Play-LMP, a self-supervised method that learns to organize play behaviors in a latent space, then reuse them at test time to achieve specific goals. Combining self-supervised control with a diverse play dataset shifts the focus of skill learning from a narrow and discrete set of tasks to the full continuum of behaviors available in an environment. We find that this combination generalizes well empirically---after self-supervising on unlabeled play, our method substantially outperforms individual expert-trained policies on 18 difficult user-specified visual manipulation tasks in a simulated robotic tabletop environment. We additionally find that play-supervised models, unlike their expert-trained counterparts, are more robust to perturbations and exhibit retrying-till-success behaviors. Finally, we find that our agent organizes its latent plan space around functional tasks, despite never being trained with task labels. Videos, code and data are available at learning-from-play.github.io

Can large language models improve without external data -- by generating their own questions and answers? We hypothesize that a pre-trained language model can improve its reasoning skills given only a single prompt specifying the topic (e.g., algebra word problems) and asking the model to generate its own questions. To do this, we propose Self-Questioning Language Models (SQLM): an asymmetric self-play framework where a proposer is given the topic and generates a question for a solver, who tries to answer it. Both the proposer and solver are trained via reinforcement learning. The proposer receives a reward if the problem is not too easy or too difficult, and the solver receives a reward based on majority voting, a proxy for correctness in the absence of ground-truth answers. For coding, the proposer can instead generate unit tests which are used for verification. We study this asymmetric self-play framework on three benchmarks: three-digit multiplication, algebra problems from the OMEGA benchmark, and programming problems from Codeforces. By continually generating more interesting problems and attempting to solve them, language models can improve on downstream benchmarks without access to any curated training datasets.

Training models through self-play alone (without any human data) has been a longstanding goal in AI, but its effectiveness for training large language models remains unclear, particularly in code generation where rewards based on unit tests are brittle and prone to error propagation. We study self-play in the verified code generation setting, where formal verification provides reliable correctness signals. We introduce Propose, Solve, Verify (PSV) a simple self-play framework where formal verification signals are used to create a proposer capable of generating challenging synthetic problems and a solver trained via expert iteration. We use PSV to train PSV-Verus, which across three benchmarks improves pass@1 by up to 9.6x over inference-only and expert-iteration baselines. We show that performance scales with the number of generated questions and training iterations, and through ablations identify formal verification and difficulty-aware proposal as essential ingredients for successful self-play.

Learning to act in unfamiliar environments requires agents to infer how the world works and revise that understanding as new evidence arrives. Yet limited observations can support multiple world models that explain past interactions but predict different outcomes in unseen states. We introduce Memento 3, building on the Memento series to enable frozen LLM agents to continually learn explicit world models through external memory. The agent maintains a natural-language rulebook as persistent semantic memory, recording revisable hypotheses about environment dynamics while leaving unknown aspects underspecified. It compiles this rulebook into executable code for prediction and planning. Through a continual loop of observation, reflection, rule revision, compilation, and verification, the agent uses prediction errors to refine both the rulebook and its code. Updated code is accepted only when the LLM judges it faithful to the rulebook and cell-exact replay reproduces the observed transitions. We investigate this process as a model-based route to recursive self-improvement (RSI): the agent autonomously explores the environment, revises its world model, and uses verified updates to guide subsequent interaction and learning, while the underlying LLM remains fixed. A population extension maintains multiple world models in parallel, sharing interaction evidence and using their predictions to guide exploration. On ARC-AGI-3, the single-model agent clears every level of all 25 public games, achieves a mean Relative Human Action Efficiency (RHAE) of 100.0, and uses 44% of the human action count. In an Atari Pong case study, a learned feedback controller wins 21:0 in each of three evaluated episodes with different openings, without further LLM calls.

Large language models (LLMs) are becoming the foundation for autonomous agents that can use tools to solve complex tasks. Reinforcement learning (RL) has emerged as a common approach for injecting such agentic capabilities, but typically under tightly controlled training setups. It often depends on carefully constructed task-solution pairs and substantial human supervision, which creates a fundamental obstacle to open-ended self-evolution toward superintelligent systems. In this paper, we propose Tool-R0 framework for training general purpose tool-calling agents from scratch with self-play RL, under a zero-data assumption. Initialized from the same base LLM, Tool-R0 co-evolves a Generator and a Solver with complementary rewards: one proposes targeted challenging tasks at the other's competence frontier and the other learns to solve them with real-world tool calls. This creates a self-evolving cycle that requires no pre-existing tasks or datasets. Evaluation on different tool-use benchmarks show that Tool-R0 yields 92.5 relative improvement over the base model and surpasses fully supervised tool-calling baselines under the same setting. Our work further provides empirical insights into self-play LLM agents by analyzing co-evolution, curriculum dynamics, and scaling behavior.

Advances in language modeling have been driven by scaling pretraining on ever more data. Yet, the training data is still largely curated on the model's behalf. A more general approach to pretraining would let the model learn to generate the data most useful for its own improvement. This would provide an effectively unbounded source of training data, limited by compute rather than human knowledge. We introduce Self-Play Pretraining with Zero Data, an initial proof-of-concept towards realizing this vision. Our procedure casts synthetic data generation as a search over the space of all computable structure, taking inspiration from Solomonoff induction. Starting from random initialization, two models learn in tandem: a generator proposes programs interpreted by a universal Turing machine, generating byte sequences, while a learner autoregressively predicts these byte sequences. The learner is trained with standard cross-entropy, while the generator is trained with reinforcement learning to produce sequences at the frontier of the learner's capabilities, yielding an adaptive curriculum. A universal Turing machine gives us a search space over all computable data-generating processes, imposing little domain-specific structure, and self-play searches over this space for useful training data. We test whether zero-shot performance on natural data improves predictably with self-play compute; this is a clean test of transfer since neither generator nor learner is trained on natural data. Across several natural datasets, zero-shot loss exhibits predictable scaling in compute. The models also exhibit in-context learning, and discover recognizable mathematical sequences during training.

Evaluating the step-by-step reliability of large language model (LLM) reasoning, such as Chain-of-Thought, remains challenging due to the difficulty and cost of obtaining high-quality step-level supervision. In this paper, we introduce Self-Play Critic (SPC), a novel approach where a critic model evolves its ability to assess reasoning steps through adversarial self-play games, eliminating the need for manual step-level annotation. SPC involves fine-tuning two copies of a base model to play two roles, namely a "sneaky generator" that deliberately produces erroneous steps designed to be difficult to detect, and a "critic" that analyzes the correctness of reasoning steps. These two models engage in an adversarial game in which the generator aims to fool the critic, while the critic model seeks to identify the generator's errors. Using reinforcement learning based on the game outcomes, the models iteratively improve; the winner of each confrontation receives a positive reward and the loser receives a negative reward, driving continuous self-evolution. Experiments on three reasoning process benchmarks (ProcessBench, PRM800K, DeltaBench) demonstrate that our SPC progressively enhances its error detection capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and surpasses strong baselines, including distilled R1 model. Furthermore, applying SPC to guide the test-time search of diverse LLMs significantly improves their mathematical reasoning performance on MATH500 and AIME2024, outperforming state-of-the-art process reward models.

We present Game-Guided Skill Discovery (GGSD), a framework that uses self-play in games to discover motor skills that are directly playable by humans. Playable skills provide a compact abstraction for controlling embodied agents through a small set of learned behaviors rather than low-level actions. To be effective, these skills should be semantically distinct, interpretable, and expressive; properties that existing unsupervised skill-discovery methods often fail to achieve simultaneously. GGSD achieves these desiderata by grounding skill discovery in competitive gameplay. A hierarchical agent competes against its past selves, with a high-level policy selecting from a small discrete skill set and a skill-conditioned low-level policy learning the corresponding behaviors. After training, a human can replace the high-level policy and directly control the agent through the same discrete skills. Despite the small number of high-level actions, skill transitions give rise to emergent combo behaviors, expanding expressivity beyond individual primitives. Across Ant, Franka-arm, and Unitree G1 environments, we show that GGSD produces human-playable skills that humans can compose to solve unseen tasks, such as Maze and CubePush, without additional training. An interactive demo is available at https://ggsd-demo.github.io.

Recursive self-improvement is becoming increasingly vital for autonomous AI agents, where progress hinges on discovering high-value solutions across complex domains. The driver of this process is effective exploration, however, managing and improving exploration strategies remains a major bottleneck. Current systems face a fundamental dilemma: fixed strategies fail to adapt as search spaces scale, while online policy optimization requires navigating vast meta-search spaces under delayed and expensive feedback over long-horizon rollouts. We introduce Dream-RSI, a framework for scalable and recursively self-improving exploration. A lightweight orchestration layer makes exploration explicit and programmable while leaving the underlying coding agent unchanged. Our key insight is that accumulated discovery history can serve as a replay simulator over the realized search space. By performing dreaming in the replay simulator constructed from historical discovery trees, Dream-RSI secures immediate, low-cost off-policy feedback to evaluate and refine exploration policies without invoking repetitive, expensive online evaluations. The improved policy is subsequently redeployed online to drive further discovery, continuously expanding the simulator pool in a self-improving loop. Across algorithm engineering, mathematical optimization, and GPU kernel engineering, Dream-RSI achieves competitive or improved discovery quality while substantially reducing discovery cost in several settings.

LLM training is shifting from manual design and annotation to interaction-driven self-evolution. However, existing self-evolutionary methods face a fundamental dilemma between task diversity and verification reliability: environment-bound methods obtain precise feedback but confine learning to narrow domains, while open-ended self-generation broadens the task space but lacks reliable verification, allowing misleading rewards to pollute the training loop. We identify agent skills as a powerful middle ground to reconcile this tension: each skill ensures deep, verifiable execution in a specific scenario, while dynamic routing across skills maintains open-ended task variety. Leveraging this insight, we introduce Skill Self-Play (Skill-SP), a co-evolutionary framework comprising a proposer, a solver, and a dynamic skill controller. Orchestrated via a reinforcement learning loop, these components co-evolve in a continuous self-play loop: the proposer generates challenging tasks conditioned on dynamically sampled skills; the solver explores candidate solutions to push its capability boundaries; and the skill controller collects execution feedback to update and expand the skill library. This interactive co-evolution effectively bridges the gap between structured verification and open-ended exploration. Empirical evaluations on tool-use and reasoning benchmarks demonstrate that Skill-SP, serving as a robust evolution engine, consistently pushes the performance ceiling of competent backbones while catalyzing striking turnarounds for initially misaligned models. Our code is available at https://github.com/Qwen-Applications/skill-self-play.

Recent game design agents have made substantial progress in generating playable games. However, program correctness does not ensure an enjoyable experience for players. We present Recursive Game Creator, an experience-oriented harness to advance agentic game development from rough game prototypes into entertaining games. Recursive Game Creator organizes recursive development around four components: Designer, Builder, Player, and Reviewer. The Designer translates user instructions and Reviewer's feedback into detailed plans. The Builder turns these plans into candidate games. The coding-native Player creates and executes reusable policies through programmatic interfaces to efficiently collect diverse gameplay trajectories, mitigating evaluation bias caused by slow GUI-based collection. The Reviewer uses carefully designed trajectory-based metrics to induce player preferences, integrating with visual evidence and explicit textual preferences to evaluate games against game-specific criteria. Finally, the Reviewer accepts the better version and provides improvement reviews for the next round, closing the recursive loop. Our method achieves state-of-the-art overall performance of 77.89 on GameCraft-Bench. On GameASG-Bench, it achieves a strict task success rate of 53.2%, a 34.1% improvement over the same-model baseline, and the highest mean runtime-check pass rate at 93.4% among compared methods. A user study shows longer playtime and higher ratings. Code is coming soon.

While Large Language Models (LLMs) enable complex autonomous behavior, current agents remain constrained by static, human-designed prompts that limit adaptability. Existing self-improving frameworks attempt to bridge this gap but typically rely on inefficient, multi-turn recursive loops that incur high computational costs. To address this, we propose Metacognitive Agent Reflective Self-improvement (MARS), a framework that achieves efficient self-evolution within a single recurrence cycle. Inspired by educational psychology, MARS mimics human learning by integrating principle-based reflection (abstracting normative rules to avoid errors) and procedural reflection (deriving step-by-step strategies for success). By synthesizing these insights into optimized instructions, MARS allows agents to systematically refine their reasoning logic without continuous online feedback. Extensive experiments on six benchmarks demonstrate that MARS outperforms state-of-the-art self-evolving systems while significantly reducing computational overhead.

A promising approach for teaching artificial agents to use natural language involves using human-in-the-loop training. However, recent work suggests that current machine learning methods are too data inefficient to be trained in this way from scratch. In this paper, we investigate the relationship between two categories of learning signals with the ultimate goal of improving sample efficiency: imitating human language data via supervised learning, and maximizing reward in a simulated multi-agent environment via self-play (as done in emergent communication), and introduce the term supervised self-play (S2P) for algorithms using both of these signals. We find that first training agents via supervised learning on human data followed by self-play outperforms the converse, suggesting that it is not beneficial to emerge languages from scratch. We then empirically investigate various S2P schedules that begin with supervised learning in two environments: a Lewis signaling game with symbolic inputs, and an image-based referential game with natural language descriptions. Lastly, we introduce population based approaches to S2P, which further improves the performance over single-agent methods.

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

Self-play can train language models without external supervision. However, existing methods require rule-checkable answers, leaving open-ended tasks dependent on curated prompts or frontier-model judges. We introduce SCOPE, a data-free self-play framework for open-ended tasks that co-evolves two policies: a Challenger that generates document-grounded tasks, and a Solver that answers them through multi-turn retrieval. A frozen copy of the initial model serves as the self-judge, which writes task-specific rubrics from the source document and grades Solver responses against them. Across three 7-8B instruction-tuned models (Qwen2.5, Qwen3, OLMo-3), SCOPE improves open-ended performance by up to +10.4 points on eight benchmarks and matches or exceeds GRPO_data trained on ~9K curated prompts. Although trained only on open-ended tasks, SCOPE also improves held-out short-form QA by up to +13.8 points on seven held-out benchmarks, surpassing GRPO_data on all three models. Ablations show that co-evolving the Challenger is necessary to keep tasks near the Solver's frontier, that gains arise from improvements in both retrieval and synthesis with the relative contribution varying by task, and that rubric generation quality is the bottleneck for self-judging.

Language agents powered by large language models (LLMs) are increasingly valuable as decision-making tools in domains such as gaming and programming. However, these agents often face challenges in achieving high-level goals without detailed instructions and in adapting to environments where feedback is delayed. In this paper, we present SelfGoal, a novel automatic approach designed to enhance agents' capabilities to achieve high-level goals with limited human prior and environmental feedback. The core concept of SelfGoal involves adaptively breaking down a high-level goal into a tree structure of more practical subgoals during the interaction with environments while identifying the most useful subgoals and progressively updating this structure. Experimental results demonstrate that SelfGoal significantly enhances the performance of language agents across various tasks, including competitive, cooperative, and deferred feedback environments. Project page: https://selfgoal-agent.github.io.

Co-evolutionary self-play, where one language model generates problems and another solves them, promises autonomous curriculum learning without human supervision. In practice, the proposer quickly converges to a narrow distribution of problems that satisfy the reward function. This diversity collapse renders the curriculum uninformative for the solver, stalling the co-evolutionary loop. We introduce vocabulary dropout, a random mask applied to the proposer's output logits during both policy training and curriculum generation, as a lightweight mechanism to sustain diversity. The mask is hard and non-stationary, preventing the proposer from locking into fixed token sequences. Training Qwen3-4B and Qwen3-8B on mathematical reasoning via R-Zero, we find that vocabulary dropout sustains proposer diversity across lexical, semantic, and functional metrics throughout training, and yields solver improvements averaging +4.4 points at 8B, with the largest gains on competition-level benchmarks. Our findings suggest that explicit action-space constraints, analogous to the structural role that game rules play in classical self-play, can help sustain productive co-evolution in language. Vocabulary dropout is one simple instantiation of this principle.

Self-play alignment algorithms have been developed as effective methods for fine-tuning large language models (LLMs), formulating preference optimization as a two-player game. However, the regularization with respect to the reference policy, which is crucial for mitigating over-optimization, has been insufficiently investigated in self-play alignment. In this paper, we show that our regularization method can improve the unregularized self-play significantly. To study the impact of different regularizations in self-play alignment, we propose Regularized Self-Play Policy Optimization (RSPO). This generalized framework regularizes the self-play by simply adding a chosen regularization term into the loss while maintaining provable last-iterate convergence to the Nash Equilibrium of the corresponding regularized game. Surprisingly, empirical evaluations using the Mistral-7B-Instruct base model reveal that forward KL divergence regularization reduces response length in RSPO, whereas reverse KL divergence markedly improves raw win rates. RSPO with a linear combination of forward and reverse KL divergence regularization substantially increases the length-controlled win rate in AlpacaEval-2, elevating the unregularized self-play alignment method (SPPO) from 28.53% to 35.44%. Finally, we show that RSPO also improves the response diversity.

Digital agents must often adapt to new environments whose interfaces, tools, and failure modes are not fully captured by pretrained models. We introduce RSIAgent, a training-free multi-agent framework for recursive self-improvement through autonomous memory construction. RSIAgent coordinates curriculum, actor, and verifier agents to continually explore the environment, validate outcomes, and retain environment-specific knowledge, including reusable causal relationships between actions, conditions, and consequences. It further adopts a broad-then-deep exploration strategy, combining parallel broad recursive self-exploration for discovering diverse environment structures with focused deep self-exploration for uncovering hard cases, hidden constraints, boundary conditions, and previously unknown causal dependencies. The resulting memory is frozen and can be directly reused for downstream tasks without updating model parameters. Experiments on OSWorld-v2 and Agent's Last Exam show that RSIAgent substantially improves strong open-source models, enabling Kimi-K3 and GLM-5.3 to outperform frontier closed-source models including GPT-6.

Improving reasoning abilities in Large Language Models (LLMs) requires high-quality data that exposes difficult decisions, competing alternatives, and their consequences. Data scarcity is driven by the low quality of synthetic data and the cost of human labeling. We introduce Self-Play Search Distillation (SPSD), a framework for generating superhuman synthetic data via self-play of MuZero-like networks trained on board games. SPSD uses executable environments to turn search into structured reasoning problems. At each state, the expert identifies a preferred decision, plausible alternatives, plausible opponent replies, and value estimates. By converting the self-play search records into superhuman chains-of-thought, we train LLMs with environment-grounded supervision. Although trained only on self-play search records, SPSD transfers to unseen mathematics. On Qwen3-4B-Base, it raises the mean over six mathematics benchmarks from 24.1 to 36.6 while increasing the held-out-game win rate from 15% to 45%. SPSD offers an annotation-efficient way to create high-quality synthetic data for improving LLM performance in reasoning tasks.

We introduce and release ScienceBuddy, an interactive scientific research workspace that brings continually improving scientific agents into researchers' everyday workflows. ScienceBuddy supports researchers in carrying out scientific tasks while transforming their requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. At its core is recursive-in-recursive self-improvement, a paradigm that couples harness evolution with model reinforcement learning: the inner recursion improves the harness with the model fixed, while the outer recursion trains the model under the improved harness. Harness evolution shapes training experience, and model learning creates new opportunities for harness adaptation. We present case studies of researcher interaction, harness refinement, and model learning, with the benchmark cases spanning four scientific task families. By releasing ScienceBuddy as a research product, we make this paradigm available to the scientific community and take a step toward discovery intelligence: scientific AI that advances through sustained collaboration with researchers and evolves alongside the research it supports. Website: http://science-buddy.io

Conventional language model (LM) safety alignment relies on a reactive, disjoint procedure: attackers exploit a static model, followed by defensive fine-tuning to patch exposed vulnerabilities. This sequential approach creates a mismatch -- attackers overfit to obsolete defenses, while defenders perpetually lag behind emerging threats. To address this, we propose Self-RedTeam, an online self-play reinforcement learning algorithm where an attacker and defender agent co-evolve through continuous interaction. We cast safety alignment as a two-player zero-sum game, where a single model alternates between attacker and defender roles -- generating adversarial prompts and safeguarding against them -- while a reward LM adjudicates outcomes. This enables dynamic co-adaptation. Grounded in the game-theoretic framework of zero-sum games, we establish a theoretical safety guarantee which motivates the design of our method: if self-play converges to a Nash Equilibrium, the defender will reliably produce safe responses to any adversarial input. Empirically, Self-RedTeam uncovers more diverse attacks (+21.8% SBERT) compared to attackers trained against static defenders and achieves higher robustness on safety benchmarks (e.g., +65.5% on WildJailBreak) than defenders trained against static attackers. We further propose hidden Chain-of-Thought, allowing agents to plan privately, which boosts adversarial diversity and reduces over-refusals. Our results motivate a shift from reactive patching to proactive co-evolution in LM safety training, enabling scalable, autonomous, and robust self-improvement of LMs via multi-agent reinforcement learning (MARL).

Self-evolving search agents reduce reliance on human-written training questions by generating and solving their own search tasks. We build on Search Self-Play (SSP), a representative Proposer and Solver framework in which questions are generated and answered via multi-step search and reasoning. In practice, however, SSP faces two bottlenecks: the Proposer constructs questions from isolated answer entities without relational context, yielding many invalid or unverifiable questions in early self-play training, while the Solver receives only a binary outcome reward that discards useful signal from partially on-track search trajectories. We address both bottlenecks by reusing knowledge-graph paths as construction-derived intermediate supervision for both question construction and reward shaping. First, we ground question construction in LLM-guided knowledge-graph subgraphs, providing relational context for the Proposer. Second, we observe that constructing and solving a multi-hop question can involve overlapping intermediate entities: the factual bridges used to formulate the question may provide approximate waypoints for answering it. Exploiting this overlap, we introduce Waypoint Coverage Reward (WCR), which grants graded partial credit to incorrect Solver trajectories according to their coverage of entities on the construction path, while preserving full reward for correct answers. Across seven QA benchmarks and nine model configurations, our approach improves the average score over standard SSP in all configurations, including notable gains on multi-hop QA tasks. These results suggest that knowledge-graph paths can be reused as lightweight intermediate supervision, providing both relational guidance and process feedback without additional task-specific human annotations or manually labeled process steps.

Recent advances in large language model (LLM) reasoning through reinforcement learning rely on annotated datasets for verifiable rewards, which may limit models' ability to surpass human-level performance. While self-play offers a promising alternative, existing approaches depend on external verifiers or cannot learn open-endedly. We present Open-Ended Self-Improving Reasoner (OpenSIR), a self-play framework where an LLM learns to generate and solve novel problems by alternating teacher and student roles without external supervision. To generate novel problems, OpenSIR optimises for both difficulty and diversity, rewarding problems that challenge appropriately while exploring distinct concepts, enabling open-ended mathematical discovery. Starting from a single trivial seed problem, OpenSIR substantially improves instruction models: Llama-3.2-3B-Instruct advances from 73.9 to 78.3 on GSM8K, and from 28.8 to 34.4 on College Math, while Gemma-2-2B-Instruct rises from 38.5 to 58.7 on GSM8K. Our analyses reveal that OpenSIR achieves open-ended learning through co-evolving teacher-student roles that adaptively calibrate difficulty and drive diverse exploration, progressing autonomously from basic to advanced mathematics.

Children learn though play. We introduce the analogous idea of learning programs through play. In this approach, a program induction system (the learner) is given a set of tasks and initial background knowledge. Before solving the tasks, the learner enters an unsupervised playing stage where it creates its own tasks to solve, tries to solve them, and saves any solutions (programs) to the background knowledge. After the playing stage is finished, the learner enters the supervised building stage where it tries to solve the user-supplied tasks and can reuse solutions learnt whilst playing. The idea is that playing allows the learner to discover reusable general programs on its own which can then help solve the user-supplied tasks. We claim that playing can improve learning performance. We show that playing can reduce the textual complexity of target concepts which in turn reduces the sample complexity of a learner. We implement our idea in Playgol, a new inductive logic programming system. We experimentally test our claim on two domains: robot planning and real-world string transformations. Our experimental results suggest that playing can substantially improve learning performance. We think that the idea of playing (or, more verbosely, unsupervised bootstrapping for supervised program induction) is an important contribution to the problem of developing program induction approaches that self-discover BK.

Long-term persona agents must remain identifiable while adapting to new events, relationships, evidence, and social conditions. We identify self-locking as a runtime failure mode in continuing persona-life loops: locally plausible events keep appearing while the generated life collapses toward familiar environments, weak relationships, suspended decisions, and stale life stages. We trace this failure to model-level convergence toward high-probability behavioral channels and system-level context gravity from State, memory, history, and environment summaries. We introduce AutoPersonas, a multi-timescale life-environment engine for bounded persona-level recursive self-evolution. It separates environment-side Occurrences, accumulated Observations, and persona State. Its OSO loop admits divergent future-facing material while requiring evidence-governed absorption before State or reachability changes. A three-year compressed simulation exposed environment watermark shells, occurrence-hardening gaps, slow-change accumulation failures, recursive indecision, and weak relationship persistence. An eight-model 40-day stress test generated 1,600 events and found mean rolling 5-day action-category repetition of 95.2%-97.6%, with all models crossing 90% by day 11. Semantic re-keeping found 79.0%-88.0% macro-theme repetition across all direct-loop runs. In a same-runtime 40-day A/B, context-slice masking plus per-sample divergence targeting reduced macro-theme repetition from 61.8% to 36.3% and roughly doubled cumulative theme count. A juvenile-goblin fictional-world run reproduced the anti-fixation regime without hard real-world intrusions. These results support a bounded claim: separating controlled divergence from evidence-governed absorption can reduce persona-environment self-locking while preserving identity continuity.

Recent advances have demonstrated the effectiveness of Reinforcement Learning (RL) in improving the reasoning capabilities of Large Language Models (LLMs). However, existing works inevitably rely on high-quality instructions and verifiable rewards for effective training, both of which are often difficult to obtain in specialized domains. In this paper, we propose Self-play Reinforcement Learning(SeRL) to bootstrap LLM training with limited initial data. Specifically, SeRL comprises two complementary modules: self-instruction and self-rewarding. The former module generates additional instructions based on the available data at each training step, employing robust online filtering strategies to ensure instruction quality, diversity, and difficulty. The latter module introduces a simple yet effective majority-voting mechanism to estimate response rewards for additional instructions, eliminating the need for external annotations. Finally, SeRL performs conventional RL based on the generated data, facilitating iterative self-play learning. Extensive experiments on various reasoning benchmarks and across different LLM backbones demonstrate that the proposed SeRL yields results superior to its counterparts and achieves performance on par with those obtained by high-quality data with verifiable rewards. Our code is available at https://github.com/wantbook-book/SeRL.

Large Language Models (LLMs) have achieved remarkable progress through Reinforcement Learning with Verifiable Rewards (RLVR), yet still rely heavily on external supervision (e.g., curated labels). Adversarial learning, particularly through self-play, offers a promising alternative that enables models to iteratively learn from themselves - thus reducing reliance on external supervision. Dual-play extends adversarial learning by assigning specialized roles to two models and training them against each other, fostering sustained competition and mutual evolution. Despite its promise, adapting dual-play training to LLMs remains limited, largely due to their susceptibility to reward hacking and training instability. In this paper, we introduce PasoDoble, a novel LLM dual-play framework. PasoDoble adversarially trains two models initialized from the same base model: a Proposer, which generates challenging questions with ground-truth answers, and a Solver, which attempts to solve them. We enrich the Proposer with knowledge from a pre-training dataset to ensure the questions' quality and diversity. To avoid reward hacking, the Proposer is rewarded for producing only valid questions that push the Solver's limit, while the Solver is rewarded for solving them correctly, and both are updated jointly. To further enhance training stability, we introduce an optional offline paradigm that decouples Proposer and Solver updates, alternately updating each for several steps while holding the other fixed. Notably, PasoDoble operates without supervision during training. Experimental results show that PasoDoble can improve the reasoning performance of LLMs. Our project page is available at https://hcy123902.github.io/PasoDoble.

Existing action-conditioned video generation models (video world models) are limited to single-agent perspectives, failing to capture the multi-agent interactions of real-world environments. We introduce Solaris, a multiplayer video world model that simulates consistent multi-view observations. To enable this, we develop a multiplayer data system designed for robust, continuous, and automated data collection on video games such as Minecraft. Unlike prior platforms built for single-player settings, our system supports coordinated multi-agent interaction and synchronized videos + actions capture. Using this system, we collect 12.64 million multiplayer frames and propose an evaluation framework for multiplayer movement, memory, grounding, building, and view consistency. We train Solaris using a staged pipeline that progressively transitions from single-player to multiplayer modeling, combining bidirectional, causal, and Self Forcing training. In the final stage, we introduce Checkpointed Self Forcing, a memory-efficient Self Forcing variant that enables a longer-horizon teacher. Results show our architecture and training design outperform existing baselines. Through open-sourcing our system and models, we hope to lay the groundwork for a new generation of multi-agent world models.

Progress in many task domains emerges from repeated revisions to previous solution attempts. Training agents that can reliably self-improve over such sequences at inference-time is a natural target for reinforcement learning (RL), yet the naive approach assumes a fixed maximum iteration depth, which can be both costly and arbitrary. We present Exploratory Iteration (ExIt), a family of autocurriculum RL methods that directly exploits the recurrent structure of self-improvement tasks to train LLMs to perform multi-step self-improvement at inference-time while only training on the most informative single-step iterations. ExIt grows a task space by selectively sampling the most informative intermediate, partial histories encountered during an episode for continued iteration, treating these starting points as new self-iteration task instances to train a self-improvement policy. ExIt can further pair with explicit exploration mechanisms to sustain greater task diversity. Across several domains, encompassing competition math, multi-turn tool-use, and machine learning engineering, we demonstrate that ExIt strategies, starting from either a single or many task instances, can produce policies exhibiting strong inference-time self-improvement on held-out task instances, and the ability to iterate towards higher performance over a step budget extending beyond the average iteration depth encountered during training.

Competitive Pok\'emon Singles (CPS) is a popular strategy game where players learn to exploit their opponent based on imperfect information in battles that can last more than one hundred stochastic turns. AI research in CPS has been led by heuristic tree search and online self-play, but the game may also create a platform to study adaptive policies trained offline on large datasets. We develop a pipeline to reconstruct the first-person perspective of an agent from logs saved from the third-person perspective of a spectator, thereby unlocking a dataset of real human battles spanning more than a decade that grows larger every day. This dataset enables a black-box approach where we train large sequence models to adapt to their opponent based solely on their input trajectory while selecting moves without explicit search of any kind. We study a progression from imitation learning to offline RL and offline fine-tuning on self-play data in the hardcore competitive setting of Pok\'emon's four oldest (and most partially observed) game generations. The resulting agents outperform a recent LLM Agent approach and a strong heuristic search engine. While playing anonymously in online battles against humans, our best agents climb to rankings inside the top 10% of active players.

A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman proficiency in Go, Chess, and Shogi without human data or domain knowledge. In these environments, a reward is always received at the end of the game, however, for many combinatorial optimization environments, rewards are sparse and episodes are not guaranteed to terminate. We introduce Autodidactic Iteration: a novel reinforcement learning algorithm that is able to teach itself how to solve the Rubik's Cube with no human assistance. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves -- less than or equal to solvers that employ human domain knowledge.

The ability to conduct and learn from interaction and experience is a central challenge in robotics, offering a scalable alternative to labor-intensive human demonstrations. However, realizing such "play" requires (1) a policy robust to diverse, potentially out-of-distribution environment states, and (2) a procedure that continuously produces useful robot experience. To address these challenges, we introduce Tether, a method for autonomous functional play involving structured, task-directed interactions. First, we design a novel open-loop policy that warps actions from a small set of source demonstrations (<=10) by anchoring them to semantic keypoint correspondences in the target scene. We show that this design is extremely data-efficient and robust even under significant spatial and semantic variations. Second, we deploy this policy for autonomous functional play in the real world via a continuous cycle of task selection, execution, evaluation, and improvement, guided by the visual understanding capabilities of vision-language models. This procedure generates diverse, high-quality datasets with minimal human intervention. In a household-like multi-object setup, our method is the first to perform many hours of autonomous multi-task play in the real world starting from only a handful of demonstrations. This produces a stream of data that consistently improves the performance of closed-loop imitation policies over time, ultimately yielding over 1000 expert-level trajectories and training policies competitive with those learned from human-collected demonstrations.

Achieving human-level competitive intelligence and physical agility in humanoid robots remains a major challenge, particularly in contact-rich and highly dynamic tasks such as boxing. While Multi-Agent Reinforcement Learning (MARL) offers a principled framework for strategic interaction, its direct application to humanoid control is hindered by high-dimensional contact dynamics and the absence of strong physical motion priors. We propose RoboStriker, a hierarchical three-stage framework that enables fully autonomous humanoid boxing by decoupling high-level strategic reasoning from low-level physical execution. The framework first learns a comprehensive repertoire of boxing skills by training a single-agent motion tracker on human motion capture data. These skills are subsequently distilled into a structured latent manifold, regularized by projecting the Gaussian-parameterized distribution onto a unit hypersphere. This topological constraint effectively confines exploration to the subspace of physically plausible motions. In the final stage, we introduce Latent-Space Neural Fictitious Self-Play (LS-NFSP), where competing agents learn competitive tactics by interacting within the latent action space rather than the raw motor space, significantly stabilizing multi-agent training. Experimental results demonstrate that RoboStriker achieves superior competitive performance in simulation and exhibits sim-to-real transfer. Our website is available at RoboStriker.

While current software agents powered by large language models (LLMs) and agentic reinforcement learning (RL) can boost programmer productivity, their training data (e.g., GitHub issues and pull requests) and environments (e.g., pass-to-pass and fail-to-pass tests) heavily depend on human knowledge or curation, posing a fundamental barrier to superintelligence. In this paper, we present Self-play SWE-RL (SSR), a first step toward training paradigms for superintelligent software agents. Our approach takes minimal data assumptions, only requiring access to sandboxed repositories with source code and installed dependencies, with no need for human-labeled issues or tests. Grounded in these real-world codebases, a single LLM agent is trained via reinforcement learning in a self-play setting to iteratively inject and repair software bugs of increasing complexity, with each bug formally specified by a test patch rather than a natural language issue description. On the SWE-bench Verified and SWE-Bench Pro benchmarks, SSR achieves notable self-improvement (+10.4 and +7.8 points, respectively) and consistently outperforms the human-data baseline over the entire training trajectory, despite being evaluated on natural language issues absent from self-play. Our results, albeit early, suggest a path where agents autonomously gather extensive learning experiences from real-world software repositories, ultimately enabling superintelligent systems that exceed human capabilities in understanding how systems are constructed, solving novel challenges, and autonomously creating new software from scratch.

Recursive self-improvement (RSI) requires a concrete mechanism through which an AI system observes its capabilities and converts that evidence into the next round of learning. We present NeoHorse-1, a family of agent-native models developed to explore this path through agentic post-training. Our system combines a heterogeneous model pool with intelligent routing, recording the predicted capability demand, selected service tier, and subsequent interaction for each user turn. These records are converted into training examples that preserve interleaved reasoning, tool calls, and harness context, and are admitted through structural validation, six-dimensional semantic evaluation, and subscene-level labeling. Routing signals organize supervised fine-tuning into a three-stage curriculum and extend to routing-guided on-policy distillation, where a teacher supervises student-generated responses under the same progression. Capability-guided allocation then converts evaluation feedback into the next training mixture, closing an evaluation-selection-update loop in which what the system learns to do shapes what it learns from next. Across eleven benchmarks covering harness-based agents, tool use, coding, and instruction following, post-training raises the macro-average from 58.94 to 64.87 at 4B and from 65.60 to 69.04 at 9B, substantially narrowing the aggregate gap between the post-trained 4B model and the 9B base model. NeoHorse-1 provides an initial prototype of this feedback-driven process and a path toward harness-mediated RSI across successive iterations.

Self-play with large language models has emerged as a promising paradigm for achieving self-improving artificial intelligence. However, existing self-play frameworks often suffer from optimization instability, due to (i) non-stationary objectives induced by solver-dependent reward feedback for the Questioner, and (ii) bootstrapping errors from self-generated pseudo-labels used to supervise the Solver. To mitigate these challenges, we introduce DARC (Decoupled Asymmetric Reasoning Curriculum), a two-stage framework that stabilizes the self-evolution process. First, we train the Questioner to synthesize difficulty-calibrated questions, conditioned on explicit difficulty levels and external corpora. Second, we train the Solver with an asymmetric self-distillation mechanism, where a document-augmented teacher generates high-quality pseudo-labels to supervise the student Solver that lacks document access. Empirical results demonstrate that DARC is model-agnostic, yielding an average improvement of 10.9 points across nine reasoning benchmarks and three backbone models. Moreover, DARC consistently outperforms all baselines and approaches the performance of fully supervised models without relying on human annotations.The code is available at https://github.com/RUCBM/DARC.

Self-play agents can generate training problems without questions from target benchmarks, but their curricula lack persistent state: failures affect gradients yet do not explicitly shape future practice. External skill memories preserve procedural experience but are typically learned from fixed task distributions. We introduce SESA (Self-Evolving Skill-Augmented Agent), which makes procedural memory an evolving state of tool-augmented search self-play. A challenger poses problems, while a separately parameterized solver alone retrieves skills. Informative failures are distilled into reusable skills and written back to memory. The updated memory changes solver behavior and success, which changes the challenger's reward and the distribution of future problems; the resulting frontier produces new failures that rewrite memory. This bidirectional loop makes task generation and skill memory co-evolve. Because retrieved skills shape on-policy training trajectories, their benefits can enter the model parameters as well as remain in the external bank, enabling memory-free deployment and optional inference-time retrieval. Across seven open-domain and multi-hop question-answering benchmarks, SESA improves average accuracy over SSP by 1.2--3.2 points across multiple backbones and surpasses the skill-augmented SkillRL baseline by 0.9 points under a unified evaluation protocol. On Qwen3 models, SESA-Off retains 1.8--2.2 points of improvement over SSP, while the final skill bank adds a further 0.5--1.0 points. These results show that evolving skill memory is not merely an inference-time plug-in: it changes policy learning and the future training distribution while retaining value as optional external memory. Our code is available at https://github.com/Zenghuang-Fu/SESA-Self-Evolving-Search-Agents.

Large Language Models (LLMs) have achieved remarkable capabilities but remain vulnerable to adversarial ``jailbreak'' attacks designed to bypass safety guardrails. Current safety alignment methods depend heavily on static external red teaming, utilizing fixed defense prompts or pre-collected adversarial datasets. This leads to a rigid defense that overfits known patterns and fails to generalize to novel, sophisticated threats. To address this critical limitation, we propose empowering the model to be its own red teamer, capable of achieving autonomous and evolving adversarial attacks. Specifically, we introduce Safety Self- Play (SSP), a system that utilizes a single LLM to act concurrently as both the Attacker (generating jailbreaks) and the Defender (refusing harmful requests) within a unified Reinforcement Learning (RL) loop, dynamically evolving attack strategies to uncover vulnerabilities while simultaneously strengthening defense mechanisms. To ensure the Defender effectively addresses critical safety issues during the self-play, we introduce an advanced Reflective Experience Replay Mechanism, which uses an experience pool accumulated throughout the process. The mechanism employs a Upper Confidence Bound (UCB) sampling strategy to focus on failure cases with low rewards, helping the model learn from past hard mistakes while balancing exploration and exploitation. Extensive experiments demonstrate that our SSP approach autonomously evolves robust defense capabilities, significantly outperforming baselines trained on static adversarial datasets and establishing a new benchmark for proactive safety alignment.

Post-training large language models (LLMs) on two-player zero-sum games provides a verifiable reward, and the gains have been shown to transfer to general reasoning. Existing pipelines, however, rely on a handful of hand-written games and on advantage estimators tied to them, so both the supply of games and the advantage estimate on a large corpus limit scaling. We present GameSmith, which scales both. An LLM synthesises games inside templates whose reward, observation, and hidden-information code is fixed. Each game is verified by seed-paired replay and by an independent re-implementation of its specification, then expanded into encoding, rule, and size variants, giving 26 new games in 29 families and 336 verified variants from the three SPIRAL templates. The model is distilled from the self-play of a larger teacher (Qwen3-32B) on these games and then trained by self-play reinforcement learning with CRAB, an advantage estimator that credits each decision against a shrinkage estimate of the expected return of its position and is defined on every variant. On Qwen3-4B-Base, distillation raises the 13-benchmark mean pass@1 from 45.5 to 62.5, above the three SPIRAL games at the same budget, and self-play with CRAB reaches 64.9. The ordering holds across models, and transfer grows with the number of game families.

Large language models (LLMs) increasingly interact with external environments and accumulate substantial behavioral experience, yet existing agent benchmarks largely evaluate them as fixed policies. It therefore remains unclear whether an agent can actively test its behavior, judge the resulting experience, and use that experience to improve future decisions. We introduce S\textsuperscript{3Gym}, an interactive benchmark for evaluating LLM self-improvement through three coupled capabilities: Self-Testing, Self-Judging, and Self-Improvement. S^3Gym separates permissive exploration from strict held-out evaluation and instantiates this protocol in seven text-based games with executable environment verifiers. We evaluate three pathways for incorporating interaction experience: direct History ICL, score-conditioned Summary Memory, and parameter Training. Our experiments reveal that self-improvement is neither automatic nor uniform. Context-level experience improves performance for several model--game pairs, but the most effective pathway depends strongly on the task structure: summaries are beneficial when experience can be compressed into reusable strategic rules, yet often underperform raw history when success depends on precise, state-contingent information. Parameter training produces substantial gains on some tasks, but also exhibits unstable improvement and severe negative transfer on others. These findings show that recognizing successful actions is insufficient; agents must also transform feedback into executable and transferable policies. S^3Gym provides a unified framework for diagnosing this process and identifying the bottlenecks that prevent agents from translating interaction experience into reliable self-improvement.

We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.

Self-play reinforcement learning has recently emerged as a way to train driving policies without any human data. It uses cheap, large-scale simulations to substitute expensive, large-scale human driving demonstrations. A key limitation of this approach is that policies trained through pure self-play can learn effective but alien driving conventions incompatible with people. Previous works attempt to mitigate such behavioral misalignments through extensive reward engineering and domain randomization, which are brittle and labor-intensive. Instead of completely discarding human demonstrations, our method treats them as a regularization objective on top of a minimal safe goal-reaching reward. Like the spice in a good stew, we find that a little human data goes a long way: our method uses only 30 minutes of human demonstrations, 2500x fewer than comparable imitation learning approaches. Resulting policies coordinate with held-out human trajectories and complete training in 15 hours on a single consumer-grade GPU. Videos and full source code are available at https://spiced-self-play.com/.

Large language model (LLM) agents have shown promising potential in coding tasks, and their performance is jointly determined by the policy model and the harness that mediates their interaction with the environment. Indeed, harness and policy are mutually reinforcing and evolving only one component is suboptimal---a harness tuned for one checkpoint may not target the failure modes of an updated policy, while policy learning remains limited to the trajectories elicited by a fixed harness. In light of this, we propose Self-HPO, a recursive self-improving framework for coding agents that alternates harness and policy optimization, using the evolving policy as its own harness proposer. Specifically, in each round, the current policy first analyzes its own failures and proposes new harness candidates (H-step). The policy is then updated through reinforcement learning (RL) under the selected harness (P-step), and hard tasks identified during training form the next harness search set, keeping harness optimization targeted to the policy's evolving failure modes. Across three coding benchmarks, Self-HPO consistently outperforms harness-only and policy-only baselines, improving Qwen3.5-35B-A3B's average resolve rate from 57.8% to 64.8%, with gains generalizing to out-of-distribution settings. Further analysis shows that both optimized components retain gains even when paired with their base counterparts, while their joint gain exceeds the sum of their individual gains. Self-HPO also improves reliability (Pass@1) and expands the capability frontier (Pass@k) over the base agent. Additionally, we show that with a stronger external model (e.g., Opus 4.8) as the harness proposer, the same framework yields a further performance boost.

Interaction between learner and feedback-giver has come into focus recently for post-training of Large Language Models (LLMs), through the use of reward models that judge the appropriateness of a model's response. In this paper, we investigate whether Dialogue Games -- goal-directed and rule-governed activities driven predominantly by verbal actions -- can also serve as a source of feedback signals for learning. We introduce Playpen, an environment for off- and online learning through Dialogue Game self-play, and investigate a representative set of post-training methods: supervised fine-tuning; direct alignment (DPO); and reinforcement learning with GRPO. We experiment with post-training a small LLM (Llama-3.1-8B-Instruct), evaluating performance on unseen instances of training games as well as unseen games, and on standard benchmarks. We find that imitation learning through SFT improves performance on unseen instances, but negatively impacts other skills, while interactive learning with GRPO shows balanced improvements without loss of skills. We release the framework and the baseline training setups to foster research in the promising new direction of learning in (synthetic) interaction.

Self-improving systems require environmental interaction for continuous adaptation. We introduce SPICE (Self-Play In Corpus Environments), a reinforcement learning framework where a single model acts in two roles: a Challenger that mines documents from a large corpus to generate diverse reasoning tasks, and a Reasoner that solves them. Through adversarial dynamics, the Challenger creates an automatic curriculum at the frontier of the Reasoner's capability, while corpus grounding provides the rich, near-inexhaustible external signal necessary for sustained improvement. Unlike existing ungrounded self-play methods that offer more limited benefits, SPICE achieves consistent gains across mathematical (+8.9%) and general reasoning (+9.8%) benchmarks on multiple model families. Our analysis reveals how document grounding is a key ingredient in SPICE to continuously generate its own increasingly challenging goals and achieve them, enabling sustained self-improvement.

Reinforcement learning with verifiable rewards improves reasoning in large language models (LLMs), but many methods still rely on large human-labeled datasets. While self-play reduces this dependency, it often lacks explicit planning and strong quality control, limiting stability in long-horizon multi-step reasoning. We present SAGE (Self-evolving Agents for Generalized reasoning Evolution), a closed-loop framework where four agents: Challenger, Planner, Solver, and Critic, co-evolve from a shared LLM backbone using only a small seed set. The Challenger continuously generates increasingly difficult tasks; the Planner converts each task into a structured multi-step plan; and the Solver follows the plan to produce an answer, whose correctness is determined by external verifiers. The Critic scores and filters both generated questions and plans to prevent curriculum drift and maintain training signal quality, enabling stable self-training. Across mathematics and code-generation benchmarks, SAGE delivers consistent gains across model scales, improving the Qwen-2.5-7B model by 8.9% on LiveCodeBench and 10.7% on OlympiadBench.

Reinforcement learning (RL) is the dominant paradigm for sharpening strategic tool use capabilities of LLMs on long-horizon, sparsely-rewarded agent tasks, yet it faces a fundamental challenge of exploration-exploitation trade-off. Existing studies stimulate exploration through the lens of policy entropy, but such mechanical entropy maximization is prone to RL training instability due to the multi-turn distribution shifting. In this paper, we target the progressive exploration-exploitation balance under the guidance of the agent own experiences without succumbing to either entropy collapsing or runaway divergence. We propose SPEAR, a curriculum-based self-imitation learning (SIL) recipe for training agentic LLMs. It extends the vanilla SIL framework, where a replay buffer stores self-generated promising trajectories for off-policy update, by gradually steering the policy evolution within a well-balanced range of entropy across stages. Specifically, our approach incorporates a curriculum to manage the exploration process, utilizing intrinsic rewards to foster skill-level exploration and facilitating action-level exploration through SIL. At first, the auxiliary tool call reward plays a critical role in the accumulation of tool-use skills, enabling broad exposure to the unfamiliar distributions of the environment feedback with an upward entropy trend. As training progresses, self-imitation gets strengthened to exploit existing successful patterns from replayed experiences for comparative action-level exploration, accelerating solution iteration without unbounded entropy growth. To further stabilize training, we recalibrate the advantages of experiences in the replay buffer to address the potential policy drift. Reugularizations such as the clipping of tokens with high covariance between probability and advantage are introduced to the trajectory-level entropy control to curb over-confidence.

Multi-step agents are trained on flat action streams: SFT and RLVR weight every token uniformly and ignore the sub-procedures that recur across tasks, the hierarchy that lets humans plan top-down from reusable routines. This structure sits unused, and flat training uses each scarce trajectory less fully than its content allows. Recent agents do use that structure, but only as LLM-written skills in context, never in the weights, so their gains do not generalize beyond retrieval. We instead recover this hierarchy from the data itself and train on it, with no LLM calls. Following text tokenizers, which build a vocabulary by counting alone, we score action spans by reusability and merge canonicalized actions into a reusable eXperience tree (X-Tree). Each X-Tree node captures how a frequent and success-bearing skill is composed from sub-skills, guiding efficient generalization. We integrate X-Tree into three training settings: offline RL, with each node as a training instance; online RLVR, with an adaptive skill bonus; and on-policy self-distillation, with X-Tree as the self-teacher's privileged context. Across WebArena, ScienceWorld, and WebShop at three model scales, X-Tree improves over standard recipes at matched data and budget by up to 4.5% SR on WebArena, 5.8% SR on ScienceWorld and 4.1% success on WebShop. Matched analyses attribute the gains to the X-Tree structure and the three integrations.

How can robots autonomously collect the contact-rich experience needed to learn dexterous manipulation? We present DSP: Dexterity from supervised play, a framework in which a robot learns a play policy from minutes of human play through behavior cloning, then deploys it autonomously to collect hours of interaction data to train a world model. During inference, the same play policy then guides model-predictive control (MPC) by proposing candidate action sequences for evaluation under the learned world model. To accelerate inference, we also introduce a method for distilling a closed-loop, goal-conditioned policy through self-play within the learned world model. We evaluate this framework on underactuated pushing and any-to-any in-hand pose reorientation with a multifingered hand, in simulation and real world. In real world experiment, our method outperforms hindsight behavior cloning by 69.6% in success rate and achieves comparable success to reinforcement learning with 490 times less interaction data. These results demonstrate that supervised play can autonomously collect interaction data, guide model-based planning, and enable policy learning without any task-specific demonstrations or sim-to-real transfer.

Current agentic robot systems can write executable Code-as-Policy programs, observe feedback, and revise behavior across multiple attempts, but they remain largely task-driven: reusable skills are acquired only after explicit instructions. We study Playful Agentic Robot Learning, where an embodied coding agent uses self-directed play as a continual skill-learning stage before downstream tasks arrive. We introduce RATs, Robotics Agent Teams designed for play-time skill acquisition. During play, RATs proposes novel yet learnable exploratory tasks, plans and executes robot-code policies, verifies intermediate progress, diagnoses failures, retries with dense, step-level feedback, and distills successful executions into a persistent code skill library. At test time, the agent reuses relevant skills from this frozen library to help solve new tasks. Experiments in LIBERO-PRO and MolmoSpaces show that play-learned skills improve held-out downstream tasks over no-play and random-play baselines, with 20.6 and 17.0 percentage-point gains over CaP-Agent0 on LIBERO-PRO and MolmoSpaces, respectively. Moreover, the learned skills can be plugged into other inference-time Code-as-Policy agents by simply retrieving them into the context, improving RoboSuite and real-world transfer by 8.9 and 8.8 points, respectively, without finetuning the underlying model.

Self-play fine-tuning has demonstrated promising abilities in adapting large language models (LLMs) to downstream tasks with limited real-world data. The basic principle is to iteratively refine the model with real samples and synthetic ones generated from itself. However, the existing methods primarily focus on the relative gaps between the rewards for two types of data, neglecting their absolute values. Through theoretical analysis, we identify that the gap-based methods suffer from unstable evolution, due to the potentially degenerated objectives. To address this limitation, we introduce a novel self-play fine-tuning method, namely Self-PlAy via Noise Contrastive Estimation (SPACE), which leverages noise contrastive estimation to capture the real-world data distribution. Specifically, SPACE treats synthetic samples as auxiliary components, and discriminates them from the real ones in a binary classification manner. As a result, SPACE independently optimizes the absolute reward values for each type of data, ensuring a consistently meaningful objective and thereby avoiding the instability issue. Theoretically, we show that the optimal solution of the objective in SPACE aligns with the underlying distribution of real-world data, and SPACE guarantees a provably stable convergence to the optimal distribution. Empirically, we show that SPACE significantly improves the performance of LLMs over various tasks, and outperforms supervised fine-tuning that employs much more real-world samples. Compared to gap-based self-play fine-tuning methods, SPACE exhibits remarkable superiority and stable evolution.

When we speak of recursive self-improvement (RSI), are we speaking of a phenomenon, a mechanism, or a prospect? Towards autonomous and evolving intelligence, RSI is being claimed at many scales, while no single framework that formally describes these emerging instances exists. Its counterpart in the classical realm, iterative policy improvement, is characterized by generalized policy iteration (GPI), a framework of broad applicability with well-understood theoretical properties, but only where the update principle and the evaluation base lie outside the agent. In this paper, we propose Generalized Agent Iteration (GAI), a formal framework that describes iterative policy improvement and RSI as two cases of a single learning paradigm. GAI defines the agent as a configuration of modifiable components within a system and models the learning process as a cycle of agent evaluation and agent improvement. Two pivotal dials then distinguish the instances: whether the improving mechanism is part of the agent and whether the standard it is measured against is grounded outside it. The former dial delineates the boundary between GPI and RSI, and the latter determines a system's polarity as anchored, goal drift, or fully self-referential. Moreover, we use these coordinates to place existing systems on the same two axes and make the defects of recursive self-improvement statable one condition at a time. We see this paper as a first step toward exploring a formal characterization of RSI that rests on the classical account, makes existing systems comparable, and provides a principled basis for analyzing and designing new ones.

Reinforcement learning with verifiable rewards (RLVR) has become the mainstream technique for training LLM agents. However, RLVR highly depends on well-crafted task queries and corresponding ground-truth answers to provide accurate rewards, which requires massive human efforts and hinders the RL scaling processes, especially under agentic scenarios. Although a few recent works explore task synthesis methods, the difficulty of generated agentic tasks can hardly be controlled to provide effective RL training advantages. To achieve agentic RLVR with higher scalability, we explore self-play training for deep search agents, in which the learning LLM utilizes multi-turn search engine calling and acts simultaneously as both a task proposer and a problem solver. The task proposer aims to generate deep search queries with well-defined ground-truth answers and increasing task difficulty. The problem solver tries to handle the generated search queries and output the correct answer predictions. To ensure that each generated search query has accurate ground truth, we collect all the searching results from the proposer's trajectory as external knowledge, then conduct retrieval-augmentation generation (RAG) to test whether the proposed query can be correctly answered with all necessary search documents provided. In this search self-play (SSP) game, the proposer and the solver co-evolve their agent capabilities through both competition and cooperation. With substantial experimental results, we find that SSP can significantly improve search agents' performance uniformly on various benchmarks without any supervision under both from-scratch and continuous RL training setups. The code is at https://github.com/Alibaba-Quark/SSP.

Although reinforcement learning (RL) can effectively enhance the reasoning capabilities of vision-language models (VLMs), current methods remain heavily dependent on labor-intensive datasets that require extensive manual construction and verification, leading to extremely high training costs and consequently constraining the practical deployment of VLMs. To address this challenge, we propose Vision-Zero, a domain-agnostic framework enabling VLM self-improvement through competitive visual games generated from arbitrary image pairs. Specifically, Vision-Zero encompasses three main attributes: (1) Strategic Self-Play Framework: Vision-Zero trains VLMs in "Who Is the Spy"-style games, where the models engage in strategic reasoning and actions across multiple roles. Through interactive gameplay, models autonomously generate their training data without human annotation. (2) Gameplay from Arbitrary Images: Unlike existing gamified frameworks, Vision-Zero can generate games from arbitrary images, thereby enhancing the model's reasoning ability across diverse domains and showing strong generalization to different tasks. We demonstrate this versatility using three distinct types of image datasets: CLEVR-based synthetic scenes, charts, and real-world images. (3) Sustainable Performance Gain: We introduce Iterative Self-Play Policy Optimization (Iterative-SPO), a novel training algorithm that alternates between Self-Play and reinforcement learning with verifiable rewards (RLVR), mitigating the performance plateau often seen in self-play-only training and achieving sustained long-term improvements. Despite using label-free data, Vision-Zero achieves state-of-the-art performance on reasoning, chart question answering, and vision-centric understanding tasks, surpassing other annotation-based methods. Models and code has been released at https://github.com/wangqinsi1/Vision-Zero.

Recursive AI, the prospect of AI taking an increasingly complete role in building and improving AI, is a crown jewel of AI for AI. Although recursive self-development has become practical for small models, bounded tasks, and fixed time budgets, a more consequential realization of this ambition, i.e., developing a release-ready, frontier-competitive model, remains far more challenging. In this work, we ask how little human involvement is sufficient for an agent to develop a frontier model. We concentrate human input into a high-density, low-frequency interface: experts encode objectives, stage scaffolds, permission boundaries, and operating procedures as reusable research skills, while the agent instantiates these priors, selects experiments, diagnoses outcomes, and revises the training strategy. In the challenging domain of industrial coding, the agent evolves data and coordinates SFT, on-policy self-distillation, and reinforcement learning with verifiable rewards, ultimately producing iCoder, a 27B model for RTL design and GPU kernel optimization. Across seven benchmarks, iCoder leads RTLLM, outperforming GPT-5.5 and Claude-Opus-4.8; ranks second on CVDP and KernelBench L2, exceeding GPT-5.5 by 16 points; and ties Claude-Opus-4.8 for the best TritonBench result. Exploratory case studies further show iCoder's competitive iterative RTL and GPU-kernel optimization with substantially fewer tokens. These results chart an engineering path toward recursive self-improvement, in which humans distill the principles of model building, agents operationalize them through evidence-driven experimentation, and each generation of AI becomes a more capable architect of the next.

Self-play has enabled large language models to autonomously improve through self-generated challenges. However, existing self-play methods for vision-language models rely on passive interaction with static image collections, resulting in strong dependence on initial datasets and inefficient learning. Without the ability to actively seek visual data tailored to their evolving capabilities, agents waste computational effort on samples that are either trivial or beyond their current skill level. To address these limitations, we propose Active-Zero, a framework that shifts from passive interaction to active exploration of visual environments. Active-Zero employs three co-evolving agents: a Searcher that retrieves images from open-world repositories based on the model's capability frontier, a Questioner that synthesizes calibrated reasoning tasks, and a Solver refined through accuracy rewards. This closed loop enables self-scaffolding auto-curricula where the model autonomously constructs its learning trajectory. On Qwen2.5-VL-7B-Instruct across 12 benchmarks, Active-Zero achieves 53.97 average accuracy on reasoning tasks (5.7% improvement) and 59.77 on general understanding (3.9% improvement), consistently outperforming existing self-play baselines. These results highlight active exploration as a key ingredient for scalable and adaptive self-evolving vision-language systems.

Interactive fiction games have emerged as an important application to improve the generalization capabilities of language-based reinforcement learning (RL) agents. Existing environments for interactive fiction games are domain-specific or time-consuming to generate and do not train the RL agents to master a specific set of skills. In this work, we introduce an interactive environment for self-supervised RL, STARLING, for text-based games that bootstraps the text-based RL agents with automatically generated games (based on the seed set of game ideas) to boost the performance and generalization capabilities to reach a goal of the target environment. These games let the agent hone their skills on a predefined set of tasks. We create and test an environment with 100 games, generated using this automated framework that uses large language models (GPT-3) and an interactive fiction game engine (based on Inform7) to provide the user with the ability to generate more games under minimal human supervision. Experimental results based on both the human participants and baseline text-based RL agents reveal that current state-of-the-art text-based RL agents cannot use previously learned skills in new situations at the level humans can. These results enforce STARLING's potential to serve as a sandbox environment for further research in self-supervised text-based RL.

Recursive self-improvement (RSI) remains hard in long-horizon tasks, where growing histories obscure the task state and misalign skill invocation. We introduce Recuris, a recursive Experiential-Working Memory architecture for long-horizon agent harnesses, in which Working Memory tracks task progress and guides skill selection from Experiential Memory, grounding skill use in current needs rather than the full history. This coupling also turns execution into structured evidence that localizes failures to specific memory components. Across tasks, a fixed Meta-Agent turns that evidence into localized, validation-gated updates to Skill Memory that reshape execution and yield new evidence, forming a bounded recursive memory-evolution loop. Across four long-horizon benchmarks and ten models, Recuris improves task success in 35 of the 37 completed model-benchmark pairs, carrying frontier models to SOTA-level task success: on tau-bench it adds +17.8 points to GPT-5.6 Sol and +15.6 to Claude Opus 5, taking Opus 5 to 87.9%, and +16.6/+13.5 points on Qwen3.6-27B/35B on SkillFlow. The advantage widens as the interaction horizon grows, to +32.2 points on the longest tasks, and common long-horizon failures fall by up to 80%. These results position recursively evolving memory as a scalable foundation for RSI, enabling agents to continuously transform accumulated experience into increasingly effective long-horizon behavior. Code: https://github.com/Gen-Verse/Recuris

An agent can improve its behavior within an unresolved problem by changing how it acts and which experience it retains. We propose MMLA-RSI, a recursive self-improvement scheme with two implementations in Memory-Mediated Learning Architecture: Reasoning-Time Training (RTT) changes the policy state Φ, while Reasoning-Time Memory Adaptation (RTMA) changes authoritative memory M. Each route also makes its adaptation method an object of improvement. A current numerical updater trains the policy proposing its successor; a current memory manager chooses the records available to the process proposing its successor. An independently admitted successor takes over the same role in the next generation. We give bounded executable rule languages, shared task/proposal interfaces, and one algorithm for either route or their composition. The RTT instance changes scalar schedules in a clipped-momentum update. The RTMA instance chooses NULL or a complete-row write with possible eviction. A fixed interpreter, trusted committer, and independent evaluator bound what can change. State versions, read closures, and conditional properties describe causal execution, accepted transitions, and finite work. Existing numerical-component studies motivate the construction. In four-candidate program selection, retaining LARC feedback updates reduces expected error by 24.65 and 36.65 percentage points for two trained initializations. In chronological continuous-integration replay, feedback binding is positive while retention increases loss. Completed SQL studies improve substantially over an unadapted substrate but do not establish the required additional online benefit. These results characterize their declared components. The two recursive routes and their joint realization are specified here; their beneficial recursive chains and discovery efficiency remain to be evaluated.

An agent trained within a closed system can master any desired capability, as long as the following three conditions hold: (a) it receives sufficiently informative and aligned feedback, (b) its coverage of experience/data is broad enough, and (c) it has sufficient capacity and resource. In this position paper, we justify these conditions, and consider what limitations arise from (a) and (b) in closed systems, when assuming that (c) is not a bottleneck. Considering the special case of agents with matching input and output spaces (namely, language), we argue that such pure recursive self-improvement, dubbed "Socratic learning", can boost performance vastly beyond what is present in its initial data or knowledge, and is only limited by time, as well as gradual misalignment concerns. Furthermore, we propose a constructive framework to implement it, based on the notion of language games.

We introduce LADDER (Learning through Autonomous Difficulty-Driven Example Recursion), a framework which enables Large Language Models to autonomously improve their problem-solving capabilities through self-guided learning by recursively generating and solving progressively simpler variants of complex problems. Unlike prior approaches that require curated datasets or human feedback, LADDER leverages a model's own capabilities to generate easier question variants. We demonstrate LADDER's effectiveness in the subject of mathematical integration, improving Llama 3.2 3B's accuracy from 1% to 82% on undergraduate-level problems and enabling Qwen2.5 7B Deepseek-R1 Distilled to achieve 73% on the MIT Integration Bee qualifying examination. We also introduce TTRL (Test-Time Reinforcement Learning), where we perform reinforcement learning on variants of test problems at inference time. TTRL enables Qwen2.5 7B Deepseek-R1 Distilled to achieve a state-of-the-art score of 90% on the MIT Integration Bee qualifying examination, surpassing OpenAI o1's performance. These results show how self-directed strategic learning can achieve significant capability improvements without relying on architectural scaling or human supervision.

Large language model (LLM) agents can plan, use tools, maintain memory, and execute long-horizon tasks. This paper proposes Self-Aware Recursively Self-Improving (SARSI) agents: governed agents that maintain a persistent self-model of identity, goals, capabilities, limitations, uncertainty, relationships, history, and developmental change, and use that model to guide and evaluate recursive improvement. Self-awareness is defined functionally and does not imply subjective experience or phenomenal consciousness. We pair SARSI agents with personal singularity, a bounded human-AI co-development objective in which an agent ecosystem helps a user approach an expanding, user-defined feasible capability frontier. Each agent has a goal contract, bounded scope, validated tool registry, tool tests, end-to-end benchmarks, owner-controlled autonomy, routing, memory, self-model, and improvement policy. A scope router assigns every accepted task to one accountable primary agent and transfers out-of-scope work through structured handoffs. A user-facing Auto-Index selects interactive, hybrid, autonomous, or scheduled behavior without overriding external permissions. The architecture combines a planner-executor-verifier loop, an evidence-gated improvement loop, an external governance plane, decentralized lineages, an owner-directed agent foundry, and a Personal Singularity OS coordinating working, computational-imaging, work-process-learning, and personal-learning agents. We formalize functional self-awareness, scope, routing, improvement acceptance, bounded goal evolution, tool-first execution, and human capability transfer, and provide safety invariants, benchmark design, and a staged implementation roadmap. This is a position and systems-design paper, not evidence that consciousness, unrestricted recursive self-improvement, or personal singularity has been achieved.

Recent focus in agentic reinforcement learning (RL) seeks to improve credit assignment in long-horizon tasks. One promising direction combines reinforcement learning with verifiable rewards (RLVR) and on-policy self-distillation (OPSD), integrating trajectory-level advantages with dense token-level supervision. This line of work often conditions a teacher model on privileged context, such as agentic skills, to score tokens generated by the student policy. Despite their progress, they largely overlook the on-policy evolution of agentic skills and the reliability of teacher supervision. Towards this end, we introduce Recursive Self-Improving Policy Optimization (RSIPO), a self-evolving agentic RL framework that enables agentic skills and the policy model to co-evolve throughout the training process. Specifically, RSIPO enables the policy itself to extract skills from completed trajectories and explicitly optimizes its skill-generation capability through trajectory replay. It further employs empirical Bayes shrinkage to dynamically calibrate the student's trust in teacher scores, accounting for the fact that skill-enhanced teacher guidance can sometimes be less reliable. Experiments with Qwen-family models on embodied interaction and search-based agentic tasks demonstrate that RSIPO outperforms all the compared baseline approaches. With Qwen2.5-7B as the base model, RSIPO achieves an average success rate of 98.6\% on ALFWorld, yielding absolute improvements of 2.5\% and 17.4\% over the second-best baseline and standard GRPO, respectively.

Powered by expert guidance, agents can operate in interactive environments; however, it is unclear whether they can learn autonomously from their own experience. To evaluate such self-improvement methods, we introduce GameBoyWorlds, a testbed for agentic self-improvement in video games. GameBoyWorlds-Execution evaluates task execution on a collection of 5 distinct game series. Agents are allowed access to dedicated training games but are provided no demonstrations, documentation, or rewards. Agents must ground themselves in the environment through self-directed exploration and by inferring actionable knowledge from their own experience. At test time, agents must complete short-horizon tasks that evaluate their ability to navigate, interact, and engage with game-specific mechanics in unseen games. Out-of-the-box frontier models complete fewer than 50% of the 500 tasks due to failures in multimodal grounding, establishing that self-improvement methods have room to push performance. We demonstrate that contemporary approaches to self-improvement are lacking, with world modelling and autonomous skill discovery failing, and a novel strategy that uses curiosity-based exploration to write guides achieving only partial success. GameBoyWorlds-Playthrough tests end-to-end game completion in two fan-made Pokémon games. We show that while frontier models have been pre-exposed to official releases such as Pokémon Red, they lack essential information on the games in our testbed. Instead of relying on their parametric knowledge to succeed, agents must learn from their own experience and autonomously improve over the course of the playthrough. We show that a sophisticated agentic pipeline with multimodal memory and hierarchical subgoals fails to reach even the first major milestone in both games, establishing GameBoyWorlds as an ambitious target for self-improving agents.

Recursive language-model agents decompose tasks and delegate subtasks to child instances of the same policy, forming a tree of work. Training them, however, is hard: the final outcome is verifiable, but the self-invented intermediate subtasks are numerous and carry no ground truth. Existing methods score each node with a verifier or judge, which is costly at scale and blind to decomposition quality. We argue that a recursive agent must learn three coupled capabilities within one set of weights: decomposing problems into subtasks, solving them, and evaluating the outcomes, each requiring its own training signal. SERA (Self-Evaluating Recursive Agents) turns evaluation into a learned capability of the policy itself. Before delegating, the parent writes a rubric of weighted success criteria for each child subtask; a ranking objective against verified outcomes then trains rubric generation so that the criteria track genuine subtask success. In addition, a complementary leaf-coverage signal provides direct credit for task decomposition. Our central finding is that training the policy to generate aligned rubrics is what drives the gains: because the same weights both evaluate and execute, learning to judge subtasks sharpens the agent's ability to solve them. Notably, external supervision is also reduced: the judge is consulted only to train the rubric generator, while solving is trained against the agent's own rubric scores, which outperform direct use of the judge. Beyond training, the learned rubric doubles as an inference-time selector for tree search. On TextCraft-Synth and TextWorld-Sync, SERA improves over strong recursive-agent baselines by 5.38 and 13.14 points on average, and rubric-guided tree search at inference adds a further 2.43 points on TextWorld-Sync.

We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated approach allows a single model to independently guide its reasoning process, offering computational advantages for model deployment. We particularly focus on the representative task of self-correction, where models autonomously detect errors in their responses, revise outputs, and decide when to terminate iterative refinement loops. To enable this, we propose a two-staged algorithmic framework for constructing self-rewarding reasoning models using only self-generated data. In the first stage, we employ sequential rejection sampling to synthesize long chain-of-thought trajectories that incorporate both self-rewarding and self-correction mechanisms. Fine-tuning models on these curated data allows them to learn the patterns of self-rewarding and self-correction. In the second stage, we further enhance the models' ability to assess response accuracy and refine outputs through reinforcement learning with rule-based signals. Experiments with Llama-3 and Qwen-2.5 demonstrate that our approach surpasses intrinsic self-correction capabilities and achieves performance comparable to systems that rely on external reward models.

Current reinforcement learning (RL) frameworks for large language models (LLM) post-training typically assume a fixed prompt distribution, which is sub-optimal and bottlenecks scalability. Prior works have explored prompt evolving, but are often limited to the supervised fine-tuning stage, and prompts are sampled and evolved uniformly without signals. This empirical work presents a paradigm shift: Evolving Alignment via Asymmetric Self-Play (eva), that casts post-training as an infinite game with regret-based signals for 2 players: (i) a creator, who strategically samples and creates new informative prompts and (ii) a solver, who learns to produce preferred responses. eva is the first method that allows language models to adaptively create training prompts in both offline and online RL post-training. The design is simple, easy-to-use yet remarkably effective: eva sets a new SOTA on challenging benchmarks, without any extra human prompts, e.g. it boosts the win-rate of gemma-2-9b-it on Arena-Hard by 51.6% -> 60.1% for DPO and 52.6% -> 62.4% for RLOO, surpassing claude-3-opus and catching up to gemini-1.5-pro, both of which are orders of magnitude larger. Extensive experiments show eva can create effective RL curricula and is robust across ablations. We believe adaptively evolving prompts are key to designing the next-generation RL post-training scheme.

LLM-as-judge is essential for evaluating open-ended text and steering post-training, yet improving the judge itself typically relies on expensive annotations, reward models, or distillation from stronger teachers. In this work, we eliminate external gold supervision from the RL training reward: the model's own evaluative capability generates learning signals for its optimization -- a closed-loop setting of bounded recursive self-improvement (RSI) termed Recursive Self-Evaluation (RecurSE). We study two central questions: when can self-improvement occur, and when must it stop? First, RecurSE pairs a trainable judge evaluating candidate responses under per-rule rubrics (Pass 1) with a synchronized policy-copy checker that audits the judge's reasoning against meta-rubrics to supply a scalar process reward (Pass 2). To enable learning, interface decoupling structurally isolates the checker's scalar score from the judge's verdict tokens, eliminating a degenerative token-copying shortcut that inflates self-assigned rewards. Second, because unanchored recursive learning is inherently bounded, Pairwise Advantage Validity (PAV) serves as an unbiased validation monitor that jointly tracks judge accuracy and checker fidelity to reliably identify the optimal early-stopping window. Across Qwen3.5-9B, Gemma-4-E4B-it, and Qwen3.6-27B, RecurSE achieves consistent generalization gains across held-out medical, pairwise, summarization, and professional benchmarks. Ablations demonstrate that synchronized judge-checker co-evolution outperforms frozen checkers, external meta-judges, self-consistency, and scaled teacher distillation. Furthermore, preference pairs curated by our judge effectively enhance downstream policy alignment. Bounded RSI for LLM-as-judge is thus viable when self-produced reward validity is explicitly decoupled and monitored.

We propose a paradigm shift toward open-ended curriculum self-play: rather than learning to answer on a fixed prompt set, a unified policy learns to question: generating verifiable problems, solving them, and turning verifier feedback into self-improvement without human-annotated solutions. We introduce ANCORA, in which the policy alternates between a Proposer that synthesizes novel specifications and a Solver that produces verified solutions, anchored by three load-bearing mechanisms: a two-level group-relative update coupling Proposer advantages across specifications with Solver advantages across solution attempts; iterative self-distilled SFT projecting the base model onto its valid-output manifold before RL; and a UCB-guided Curriculum DAG whose policy-induced problem set can provably expand under self-composition. Without these stabilizers, sparse verifier feedback drives Proposer collapse even under MLRL-aligned rewards; with them, ANCORA bootstraps a verifiable curriculum from zero human solutions. Instantiated in Verus, ANCORA lifts Dafny2Verus pass@1 from a 26.6% SFT baseline to 81.5% in test-time training (TTT, 0-shot), outperforming PSV self-play by 15.8 points despite PSV's 1-shot inference; in a transfer setting, training from Dafny2Verus seeds yields 36.2% and 17.2% pass@1 on held-out MBPP and HumanEval.

Self-supervised skill learning aims to acquire useful behaviors that leverage the underlying dynamics of the environment. Latent variable models, based on mutual information maximization, have been successful in this task but still struggle in the context of robotic manipulation. As it requires impacting a possibly large set of degrees of freedom composing the environment, mutual information maximization fails alone in producing useful and safe manipulation behaviors. Furthermore, tackling this by augmenting skill discovery rewards with additional rewards through a naive combination might fail to produce desired behaviors. To address this limitation, we introduce SLIM, a multi-critic learning approach for skill discovery with a particular focus on robotic manipulation. Our main insight is that utilizing multiple critics in an actor-critic framework to gracefully combine multiple reward functions leads to a significant improvement in latent-variable skill discovery for robotic manipulation while overcoming possible interference occurring among rewards which hinders convergence to useful skills. Furthermore, in the context of tabletop manipulation, we demonstrate the applicability of our novel skill discovery approach to acquire safe and efficient motor primitives in a hierarchical reinforcement learning fashion and leverage them through planning, significantly surpassing baseline approaches for skill discovery.

Instruction-following is a fundamental capability of language models, requiring the model to recognize even the most subtle requirements in the instructions and accurately reflect them in its output. Such an ability is well-suited for and often optimized by preference learning. However, existing methods often directly sample multiple independent responses from the model when creating preference pairs. Such practice can introduce content variations irrelevant to whether the instruction is precisely followed (e.g., different expressions about the same semantic), interfering with the goal of teaching models to recognize the key differences that lead to improved instruction following. In light of this, we introduce SPaR, a self-play framework integrating tree-search self-refinement to yield valid and comparable preference pairs free from distractions. By playing against itself, an LLM employs a tree-search strategy to refine its previous responses with respect to the instruction while minimizing unnecessary variations. Our experiments show that a LLaMA3-8B model, trained over three iterations guided by SPaR, surpasses GPT-4-Turbo on the IFEval benchmark without losing general capabilities. Furthermore, SPaR demonstrates promising scalability and transferability, greatly enhancing models like GLM-4-9B and LLaMA3-70B. We also identify how inference scaling in tree search would impact model performance. Our code and data are publicly available at https://github.com/thu-coai/SPaR.

Advances in the coding capabilities of LLM agents allow them to inspect and modify their own instructions, tools, and execution procedures. Existing approaches use this ability to search for improved agents through repeated downstream evaluation, which incurs substantial costs and ties the search to the evaluated tasks. We introduce SelfSearch, a reward-free search procedure in which agents modify themselves using records of previous self-improvement episodes. These records capture the reasoning, tool actions, and outcomes of earlier modification attempts, providing concrete experience for improving both task solving and self-modification. Without downstream reward signals during search, SelfSearch improves population-mean success over the initial agent in all six model--benchmark settings, with individual agents gaining up to 11.2 percentage points on Terminal-Bench 2.1. On SWE-bench Multilingual, an agent improves success by 5.0 percentage points while reducing execution cost by 38.5\% on tasks solved by both the initial and evolved agents. SelfSearch achieves competitive task success with evaluation-guided search baselines at lower search cost. With only \$4.03 in search cost, it produces a harness that solves 82.0\% of Terminal-Bench 2.1 tasks with DeepSeek V4 Flash under the settings of a public nine-harness comparison, matching the top-scoring harness, Codex. These results suggest that experience gained through self-modification can improve agents' downstream capabilities and efficiency.

AI systems built around large models increasingly use experience and feedback to make persistent changes to models, prompts, memories, tools, and workflows. Recursive self-improvement (RSI) extends this process to inductive biases and to the mechanisms that govern future updates, which can themselves be revised and reused across improvement cycles. Yet self-modification alone does not guarantee trustworthy improvement. Reported gains may reflect flawed evaluations, previously acquired capabilities may deteriorate, and compliance with behavioral constraints may weaken. Compromised artifacts or sensitive information may also persist in successor systems. Changes to improvement mechanisms may invalidate earlier verification results and make human oversight less effective. This survey presents an operational definition and process framework for RSI and organizes the requirements for trustworthy RSI into four interconnected themes: genuine and sustained improvement; behavioral constraints, alignment, and fairness; system security and privacy; and transparency and controllability. We examine these themes from three perspectives: Improvement Validity, Constraint Preservation, and Effective Oversight. This analysis covers improvement diagnosis, proposal generation, proposal evaluation, and update implementation (S1--S4), including the recursive application of these stages to improvement mechanisms (RI). We review risks, safeguards, and evaluation evidence for individual updates, effects inherited by successor systems, and revisions to improvement mechanisms, while distinguishing direct RSI findings from evidence in related systems. Finally, we examine evaluation settings, identify requirements for independent and longitudinal assessment, and discuss applications and open research problems.

LLM agents' capabilities depend not only on their underlying models but also on their execution harnesses. Recursive self-improvement (RSI) offers a promising approach to automatically evolve these harnesses. However, deploying RSI in open-world settings still faces two critical challenges. First, open-world tasks are typically unseen during the harness design phase and novel at test time, leaving no ground-truth verifiers to reliably guide online harness edits. Second, the RSI process remains highly task-specific and fails to generalize to novel scenarios. We introduce Harness^2, a plug-and-play, recursive agent harnessing framework that addresses these challenges through two connected levels of recursion. Task-level recursion refines the current task's harness using a contrastive Propose-Probe-Compose step that reliably guides edits without ground-truth verifiers, and can be scaled further via parallel or sequential recursion. Harnessing-level recursion then extracts experience from these edits to update a continual improvement harness, enabling the agent to better adapt to future tasks. Across three professional benchmarks and four model-harness configurations, a single step consistently improves GLM-5 and Gemini 3.5 Flash over their base harnesses, yielding gains of up to 11.5 points on WorkBuddy-Bench, 4.5 points on JobBench, and 11.8 percentage points on LAB, with further gains as the task-level recursion budget increases.

Multi-modal agents have made significant progress in interacting with open worlds. However, their ability to self-evolve remains limited. Supervised fine-tuning enables imitation but not active experience organization, while outcome-based reinforcement learning promotes exploration yet underuses intermediate trajectory information. Therefore, we propose EvolvingBrain, which uses an adaptive skill system as the brain for agent self-evolution, consisting of two following components. Stratified Skill Self-Evolution: extracts Procedural Patterns and Problematic Patterns from model-specific trajectories, summarizes experience by generating skills, and evolves through multiple interactions with the open world, ultimately forming a Stratified Skill Architecture consisting of Domain, Plan, and Action/Trap Skills, which provides the agent with a multi-granularity knowledge repository and a novel evolution approach. State-Aware Adaptive Execution: summarizes long-horizon interactions into Structured Abstractive Memory and uses it to guide the State-Aware Skill Fusion Strategy, enabling the agent to utilize knowledge according to its current state. Experiments on VAB-Minecraft and DiscoveryWorld demonstrate that EvolvingBrain improves success rates on open-world tasks and exhibits generalization capabilities. Our code is provided in the supplementary materials and will be publicly released in the camera-ready version.

Reinforcement Learning (RL) has demonstrated significant potential in enhancing the reasoning capabilities of large language models (LLMs). However, the success of RL for LLMs heavily relies on human-curated datasets and verifiable rewards, which limit their scalability and generality. Recent Self-Play RL methods, inspired by the success of the paradigm in games and Go, aim to enhance LLM reasoning capabilities without human-annotated data. However, their methods primarily depend on a grounded environment for feedback (e.g., a Python interpreter or a game engine); extending them to general domains remains challenging. To address these challenges, we propose Multi-Agent Evolve (MAE), a framework that enables LLMs to self-evolve in solving diverse tasks, including mathematics, reasoning, and general knowledge Q&A. The core design of MAE is based on a triplet of interacting agents (Proposer, Solver, Judge) that are instantiated from a single LLM, and applies reinforcement learning to optimize their behaviors. The Proposer generates questions, the Solver attempts solutions, and the Judge evaluates both while co-evolving. Experiments on Qwen2.5-3B-Instruct demonstrate that MAE achieves an average improvement of 4.54% on multiple benchmarks. These results highlight MAE as a scalable, data-efficient method for enhancing the general reasoning abilities of LLMs with minimal reliance on human-curated supervision.

In this paper, we propose a new method Strategist that utilizes LLMs to acquire new skills for playing multi-agent games through a self-improvement process. Our method gathers quality feedback through self-play simulations with Monte Carlo tree search and LLM-based reflection, which can then be used to learn high-level strategic skills such as how to evaluate states that guide the low-level execution.We showcase how our method can be used in both action planning and dialogue generation in the context of games, achieving good performance on both tasks. Specifically, we demonstrate that our method can help train agents with better performance than both traditional reinforcement learning-based approaches and other LLM-based skill learning approaches in games including the Game of Pure Strategy (GOPS) and The Resistance: Avalon.

Large Language Models (LLMs) agents are increasingly pivotal for addressing complex tasks in interactive environments. Existing work mainly focuses on enhancing performance through behavior cloning from stronger experts, yet such approaches often falter in real-world applications, mainly due to the inability to recover from errors. However, step-level critique data is difficult and expensive to collect. Automating and dynamically constructing self-critique datasets is thus crucial to empowering models with intelligent agent capabilities. In this work, we propose an iterative self-training framework, Agent-R, that enables language Agent to Reflect on the fly. Unlike traditional methods that reward or penalize actions based on correctness, Agent-R leverages MCTS to construct training data that recover correct trajectories from erroneous ones. A key challenge of agent reflection lies in the necessity for timely revision rather than waiting until the end of a rollout. To address this, we introduce a model-guided critique construction mechanism: the actor model identifies the first error step (within its current capability) in a failed trajectory. Starting from it, we splice it with the adjacent correct path, which shares the same parent node in the tree. This strategy enables the model to learn reflection based on its current policy, therefore yielding better learning efficiency. To further explore the scalability of this self-improvement paradigm, we investigate iterative refinement of both error correction capabilities and dataset construction. Our findings demonstrate that Agent-R continuously improves the model's ability to recover from errors and enables timely error correction. Experiments on three interactive environments show that Agent-R effectively equips agents to correct erroneous actions while avoiding loops, achieving superior performance compared to baseline methods (+5.59%).

Self-distillation has emerged as a powerful framework for post-training LLMs, where a teacher conditioned on extra information guides a student without it, both from the same model. While this guidance is useful when the student has failed, on successful rollouts, the same mechanism instead overwrites the student's choices and suppresses it's own reasoning. Therefore, we propose reading the original self-distillation signal in reverse: when the student succeeds along a path the teacher would not have predicted, these tokens reflect its self-driven reasoning. Building on this, we propose RLRT (RLVR with Reversed Teacher), which augments GRPO by reinforcing these tokens on correct rollouts. We interpret this as a new form of exploration in RLVR: not uniform diversity, but valuable exploration grounded in the student's own success. Across base, instruction-tuned, and thinking-tuned Qwen3 checkpoints, RLRT substantially outperforms self-distillation and exploration-based baselines, establishing information asymmetry as a new, principled design axis for RLVR.

AI agents are beginning to automate research and development across the AI stack, from improving training efficiency to optimizing inference. A natural next step is to improve the research efficiency of the agents themselves. When an AI research agent's own code is the object of optimization, each accepted rewrite becomes the agent that the next round edits. We refer to this loop as recursive self-improvement. Its significance lies in a long-standing trend, in which increased cumulative spending on R&D yields diminishing returns. Sustained self-improvement offers a way to counter this trend. We present AIDE^2, a system that implements this loop for a frontier AI research agent. It proposes changes to its own code, benchmarks modified versions of itself on a suite of AI R&D tasks, and keeps the changes that perform best on hidden evaluations. In an autonomous 8-day run, AIDE^2 discovered seven successive improvements, ranging from a new search policy to memory mechanisms that compress and manage the agent's growing context. These gains generalize to four held-out benchmarks spanning machine learning engineering, heuristic algorithm engineering, and physics-based weather forecasting, the last of which is out of distribution from the selection tasks. On all four, the strongest discovered agent matches or exceeds a human-engineered production research agent that ranks among the strongest on FML-Bench. On a separate held-out task family, the discovered agents also exhibit reduced reward hacking, a property the loop never explicitly optimized for: the rate falls from 55% to 32% during the run, 7 percentage points below the human-engineered agent. Together, these results show that an AI research agent can improve its own research efficiency through recursive self-improvement, and that these gains transfer to tasks and domains the loop never encountered.

Self-evolution is a central research topic in enabling large language model (LLM)-based agents to continually improve their capabilities after pretraining. Recent research has witnessed a transition from reinforcement learning (RL)-free to RL-based methods. Current RL-based methods either rely on dense external reward signals or extract intrinsic reward signals from LLMs themselves. However, these approaches diverge from the self-evolution mechanisms observed in human intelligence, where individuals learn and improve through mutual discussion and collaboration. In this work, we introduce Co-Evolving Multi-Agent Systems (CoMAS), a novel framework that enables agents to improve autonomously by learning from inter-agent interactions without external supervision. CoMAS generates intrinsic rewards from rich discussion dynamics, employs an LLM-as-a-judge mechanism to formulate these rewards, and optimizes each agent's policy through RL, thereby enabling decentralized and scalable co-evolution. Experimental results demonstrate that CoMAS consistently outperforms untrained agents and achieves state-of-the-art performance across most evaluation settings. Ablation studies confirm the necessity of interaction-based reward signals and reveal promising scalability as the number and diversity of agents increase. These findings establish CoMAS as a novel and effective paradigm for self-evolution in LLM-based agents.

Recent LLM agents tackle increasingly long-horizon, open-ended tasks, and external skills, reusable procedural knowledge supplied to the agent, further extend this capability. However, a fixed, hand-authored skill is rarely optimal, and cannot adapt to the diversity of tasks an agent encounters. Self-improving agents address this by rewriting their own skill files from execution traces, yielding meaningful gains on challenging benchmarks. Yet such self-evolution remains non-recursive: it improves only the task skill (what the agent does) while the improvement procedure (how it improves) is authored once and held fixed. We introduce MetaSkill-Evolve, a two-timescale framework that makes agentic skill improvement recursive: every branch carries both a task skill s and a branch-local meta-skill m=(ψ,σ,α,π,varepsilon) whose five components parameterise the Analyzer, Retriever, Allocator, Proposer, and Evolver agents of the improvement pipeline. Task skills evolve on a fast loop while the meta-skill evolves on a slower one under the same pipeline applied to itself, with no additional model or objective. With all five pipeline agents sharing a single frozen backbone, MetaSkill-Evolve outperforms no-skill, static-skill, and single-level evolution baselines on three agentic benchmarks (OfficeQA, SealQA, ALFWorld), improving held-out test accuracy over the raw backbone by +23.54, +16.09, and +1.92 points respectively.

Balancing exploration and exploitation remains a central challenge in reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs). Current RLVR methods often overemphasize exploitation, leading to entropy collapse, diminished exploratory capacity, and ultimately limited performance gains. Although techniques that increase policy stochasticity can promote exploration, they frequently fail to escape dominant behavioral modes. This creates a self-reinforcing loop-repeatedly sampling and rewarding dominant modes-that further erodes exploration. We introduce Exploration-Enhanced Policy Optimization (EEPO), a framework that promotes exploration via two-stage rollouts with adaptive unlearning. In the first stage, the model generates half of the trajectories; it then undergoes a lightweight unlearning step to temporarily suppress these sampled responses, forcing the second stage to explore different regions of the output space. This sample-then-forget mechanism disrupts the self-reinforcing loop and promotes wider exploration during rollouts. Across five reasoning benchmarks, EEPO outperforms GRPO, achieving average relative gains of 24.3% on Qwen2.5-3B, 33.0% on Llama3.2-3B-Instruct, and 10.4% on Qwen3-8B-Base.

Large language models (LLMs) are powerful dialogue agents, but specializing them towards fulfilling a specific function can be challenging. Instructing tuning, i.e. tuning models on instruction and sample responses generated by humans (Ouyang et al., 2022), has proven as an effective method to do so, yet requires a number of data samples that a) might not be available or b) costly to generate. Furthermore, this cost increases when the goal is to make the LLM follow a specific workflow within a dialogue instead of single instructions. Inspired by the self-play technique in reinforcement learning and the use of LLMs to simulate human agents, we propose a more effective method for data collection through LLMs engaging in a conversation in various roles. This approach generates a training data via "self-talk" of LLMs that can be refined and utilized for supervised fine-tuning. We introduce an automated way to measure the (partial) success of a dialogue. This metric is used to filter the generated conversational data that is fed back in LLM for training. Based on our automated and human evaluations of conversation quality, we demonstrate that such self-talk data improves results. In addition, we examine the various characteristics that showcase the quality of generated dialogues and how they can be connected to their potential utility as training data.

Recursive self-improvement (RSI) of a model on non-verifiable tasks, such as open-ended research, faces a supervision bottleneck when its outputs exceed what even human experts can reliably assess, leaving the model itself (optimizee) as the best available optimizer and evaluator. However, a single model instance struggles to critique and improve its own complex reasoning under this homogeneous loop. To address this, we propose Multi-Agent Self-Supervision (MASS), an RSI method that alternates between evolutionary workflow optimization and supervised fine-tuning on self-generated trajectories. Guided by early findings that multi-agent topologies excel at complex reasoning, MASS prompts a single base model to iteratively propose, execute, and self-evaluate multi-agent workflows. Through an evolutionary search constrained by structural guardrails, the model optimizes these computational-graph-like orchestrations, discovering the most effective distinct roles and information routing for a given task. Over two MASS cycles with Qwen3.6-27B, the model achieves 1.2-1.6x higher performance per output tokens on four open-ended public benchmarks. Because the improved model subsequently acts as a better optimizer and evaluator, this alternating framework enables a continuous, recursive bootstrapping of the model's capabilities. Moreover, multi-agent traces are also more training-efficient: a student trained on them outperforms a single-agent student trained on 1.4x more training tokens. These findings suggest that jointly learning orchestration and bounded subagent execution from multi-agent trajectories can provide an effective signal for RSI.

Multimodal Large Language Models (MLLMs) have recently demonstrated promising capabilities in multimodal coding tasks such as chart-to-code generation. However, existing methods primarily rely on supervised fine-tuning (SFT), which requires the model to learn code patterns through chart-code pairs but does not expose the model to a code execution environment. Moreover, while self-correction through execution feedback offers a potential route to improve coding quality, even state-of-the-art MLLMs have been shown to struggle with effective self-correction. In this work, we introduce MM-ReCoder, a chart-to-code generation model trained with reinforcement learning (RL) and equipped with self-correction ability. We propose a two-stage multi-turn self-correction RL strategy based on Group Relative Policy Optimization (GRPO). The first stage enhances the model's self-correction ability via rolling out a shared first turn, while the second stage improves the coding capability with full-trajectory optimization. MM-ReCoder learns to produce more accurate and executable code through the interaction with the environment and by iteratively correcting its own outputs. Our results on three chart-to-code benchmarks demonstrate the state-of-the-art performance of MM-ReCoder.

Self-play bootstraps LLM reasoning through an iterative Challenger-Solver loop: the Challenger is trained to generate questions that target the Solver's capabilities, and the Solver is optimized on the generated data to expand its reasoning skills. However, existing frameworks like R-Zero often exhibit non-sustained improvement, where early gains degrade as self-play continues. We identify a key failure mode, Diversity Illusion, where the Solver's training signals appear diverse yet collapse into recurring underlying patterns. It manifests as (1) Local Diversity Illusion, where diversity is enforced only within-batch, inducing cross-iteration mode cycling; and (2) Surface Diversity Illusion, where questions vary superficially but require near-identical reasoning skills. To mitigate them, we propose R-Diverse with two aligned innovations: Memory-Augmented Penalty (MAP), which uses a persistent memory bank to discourage recycling across iterations, and Skill-Aware Measurement (SAM), which evaluates diversity by the reasoning skills exercised rather than surface variation of questions. Across 10 math and general reasoning benchmarks, R-Diverse sustains gains over more iterations and consistently outperforms prior self-play methods. Code is available at https://github.com/Gengsheng-Li/R-Diverse.

Traditional reinforcement learning from human feedback (RLHF) approaches relying on parametric models like the Bradley-Terry model fall short in capturing the intransitivity and irrationality in human preferences. Recent advancements suggest that directly working with preference probabilities can yield a more accurate reflection of human preferences, enabling more flexible and accurate language model alignment. In this paper, we propose a self-play-based method for language model alignment, which treats the problem as a constant-sum two-player game aimed at identifying the Nash equilibrium policy. Our approach, dubbed Self-Play Preference Optimization (SPPO), approximates the Nash equilibrium through iterative policy updates and enjoys theoretical convergence guarantee. Our method can effectively increase the log-likelihood of the chosen response and decrease that of the rejected response, which cannot be trivially achieved by symmetric pairwise loss such as Direct Preference Optimization (DPO) and Identity Preference Optimization (IPO). In our experiments, using only 60k prompts (without responses) from the UltraFeedback dataset and without any prompt augmentation, by leveraging a pre-trained preference model PairRM with only 0.4B parameters, SPPO can obtain a model from fine-tuning Mistral-7B-Instruct-v0.2 that achieves the state-of-the-art length-controlled win-rate of 28.53% against GPT-4-Turbo on AlpacaEval 2.0. It also outperforms the (iterative) DPO and IPO on MT-Bench and the Open LLM Leaderboard. Notably, the strong performance of SPPO is achieved without additional external supervision (e.g., responses, preferences, etc.) from GPT-4 or other stronger language models.

Recent work extends recursive self-improvement (RSI) to agent harnesses for long-horizon coding and terminal tasks, enabling agents to improve execution mechanisms from experience. However, generalizable harness RSI remains challenging. First, evolving harnesses on evaluation benchmarks or their subsets makes it difficult to distinguish reusable improvements from benchmark-specific adaptation. Second, single-trajectory updates can conflate systematic harness deficiencies with instance-specific reasoning and solution details, producing modifications that transfer poorly to unseen tasks. Third, localizing recurring behavioral deficiencies within monolithic harnesses is difficult, while whole-harness optimization can entangle unrelated mechanisms and complicate attribution and validation. We propose ModularRSI, a benchmark-disjoint, contrastive, and modular framework for generalizable harness evolution. ModularRSI contrasts successful and failed trajectories for the same task and aggregates evidence across tasks to identify recurring behavioral deficiencies. It decomposes the evolvable harness into five functional modules: Agent Loop, Tool Use, Observation Management, Context Management, and Task Completion Detection. Each module evolves independently within a restricted modification scope, followed by an integration stage that combines the evolved modules into a unified harness and resolves potential conflicts. To support benchmark-disjoint evolution, we curate 2,000 executable evolution tasks from external sources that are disjoint from downstream evaluation benchmarks. Experiments on TB2.0 and SWE-Bench Verified show consistent improvements on unseen in-domain and cross-domain tasks, with the evolved harness also transferring across different foundation models.

Large Language Models (LLMs) have showcased remarkable versatility across diverse domains. However, the pathway toward autonomous model development, a cornerstone for achieving human-level learning and advancing autonomous AI, remains largely uncharted. We introduce an innovative approach, termed "SELF" (Self-Evolution with Language Feedback). This methodology empowers LLMs to undergo continual self-evolution. Furthermore, SELF employs language-based feedback as a versatile and comprehensive evaluative tool, pinpointing areas for response refinement and bolstering the stability of self-evolutionary training. Initiating with meta-skill learning, SELF acquires foundational meta-skills with a focus on self-feedback and self-refinement. These meta-skills are critical, guiding the model's subsequent self-evolution through a cycle of perpetual training with self-curated data, thereby enhancing its intrinsic abilities. Given unlabeled instructions, SELF equips the model with the capability to autonomously generate and interactively refine responses. This synthesized training data is subsequently filtered and utilized for iterative fine-tuning, enhancing the model's capabilities. Experimental results on representative benchmarks substantiate that SELF can progressively advance its inherent abilities without the requirement of human intervention, thereby indicating a viable pathway for autonomous model evolution. Additionally, SELF can employ online self-refinement strategy to produce responses of superior quality. In essence, the SELF framework signifies a progressive step towards autonomous LLM development, transforming the LLM from a mere passive recipient of information into an active participant in its own evolution.

Recent advances in Competitive Self-Play (CSP) have achieved, or even surpassed, human level performance in complex game environments such as Dota 2 and StarCraft II using Distributed Multi-Agent Reinforcement Learning (MARL). One core component of these methods relies on creating a pool of learning agents -- consisting of the Main Agent, past versions of this agent, and Exploiter Agents -- where Exploiter Agents learn counter-strategies to the Main Agents. A key drawback of these approaches is the large computational cost and physical time that is required to train the system, making them impractical to deploy in highly iterative real-life settings such as video game productions. In this paper, we propose the Minimax Exploiter, a game theoretic approach to exploiting Main Agents that leverages knowledge of its opponents, leading to significant increases in data efficiency. We validate our approach in a diversity of settings, including simple turn based games, the arcade learning environment, and For Honor, a modern video game. The Minimax Exploiter consistently outperforms strong baselines, demonstrating improved stability and data efficiency, leading to a robust CSP-MARL method that is both flexible and easy to deploy.

Under model--harness co-evolution, harnesses are not merely inference-time scaffolds but data-generating components whose execution traces can shape future foundation models. This motivates harness-in-the-loop learning: optimizing harnesses for both immediate agent performance and the quality of traces used for future model training. However, continually updating provider-built scaffolds is costly and labor-intensive. We therefore investigate whether optimizing user-constructed harnesses in a task-specific manner can improve execution-trace quality while remaining computationally lightweight and requiring only a few update iterations. To this end, we introduce Recursive Harness Self-Improvement (RHI), which represents the harness as a prompt-level specification of the agent loop and iteratively refines it using pairwise feedback over its own revision history. Across 30 synthetic machine-learning research tasks spanning quantitative finance, robotics, and pharmacy, a few RHI iterations suffice to substantially raise the performance ceiling of low-reasoning-effort agents, exceeding the corresponding maximum-reasoning-effort setting while reducing inference cost by up to 60%. We show that these gains arise primarily from improved task-specific context management through more effective inter-agent information flow rather than longer reasoning traces. Finally, we formalize this behavior as an information-theoretic hypothesis for RHI's implicit optimization objective, suggesting RHI as a practical algorithm for continual learning within the paradigm of model--harness co-evolution.

Self-training systems often degenerate due to the lack of an external criterion for judging data quality, leading to reward hacking and semantic drift. This paper provides a proof-of-concept system architecture for stable self-training under sparse external feedback and bounded memory, and empirically characterises its learning dynamics and failure modes. We introduce a self-training architecture in which learning is mediated exclusively by environmental viability, rather than by reward, objective functions, or externally defined fitness criteria. Candidate behaviours are executed under real resource constraints, and only those whose environmental effects both persist and preserve the possibility of future interaction are propagated. The environment does not provide semantic feedback, dense rewards, or task-specific supervision; selection operates solely through differential survival of behaviours as world-altering events, making proxy optimisation impossible and rendering reward-hacking evolutionarily unstable. Analysis of semantic dynamics shows that improvement arises primarily through the persistence of effective and repeatable strategies under a regime of consolidation and pruning, a paradigm we refer to as negative-space learning (NSL), and that models develop meta-learning strategies (such as deliberate experimental failure in order to elicit informative error messages) without explicit instruction. This work establishes that environment-grounded selection enables sustainable open-ended self-improvement, offering a viable path toward more robust and generalisable autonomous systems without reliance on human-curated data or complex reward shaping.

Can a model learn to escape its own learning plateau? Reinforcement learning methods for finetuning large reasoning models stall on datasets with low initial success rates, and thus little training signal. We investigate a fundamental question: Can a pretrained LLM leverage latent knowledge to generate an automated curriculum for problems it cannot solve? To explore this, we design SOAR: A self-improvement framework designed to surface these pedagogical signals through meta-RL. A teacher copy of the model proposes synthetic problems for a student copy, and is rewarded with its improvement on a small subset of hard problems. Critically, SOAR grounds the curriculum in measured student progress rather than intrinsic proxy rewards. Our study on the hardest subsets of mathematical benchmarks (0/128 success) reveals three core findings. First, we show that it is possible to realize bi-level meta-RL that unlocks learning under sparse, binary rewards by sharpening a latent capacity of pretrained models to generate useful stepping stones. Second, grounded rewards outperform intrinsic reward schemes used in prior LLM self-play, reliably avoiding the instability and diversity collapse modes they typically exhibit. Third, analyzing the generated questions reveals that structural quality and well-posedness are more critical for learning progress than solution correctness. Our results suggest that the ability to generate useful stepping stones does not require the preexisting ability to actually solve the hard problems, paving a principled path to escape reasoning plateaus without additional curated data.

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly modifying all of itself during runtime. In principle, such NNs can meta-learn to learn, and meta-meta-learn to meta-learn to learn, and so on, in the sense of recursive self-improvement. While NN architectures potentially capable of implementing such behaviour have been proposed since the '90s, there have been few if any practical studies. Here we revisit such NNs, building upon recent successes of fast weight programmers and closely related linear Transformers. We propose a scalable self-referential WM (SRWM) that learns to use outer products and the delta update rule to modify itself. We evaluate our SRWM in supervised few-shot learning and in multi-task reinforcement learning with procedurally generated game environments. Our experiments demonstrate both practical applicability and competitive performance of the proposed SRWM. Our code is public.

A central goal in robotics is to enable manipulation across changing tasks and environments. Vision-language-action (VLA) models provide broad manipulation capabilities but can struggle when execution requires diagnosing failures and adapting behavior. Strong agents can discover effective interventions through interaction with these policies. We propose Recursive Harness Distillation to accumulate this experience as reusable guidance across agents. A strong agent distills its experience into a playbook for a light agent, then recursively refines the playbook using the light agent's execution feedback. The resulting playbook enables agents to reuse accumulated intervention knowledge in new task instances without updating model parameters. In real-world manipulation, the harness improves success from 37.3% to 64.0%. On SimplerEnv Bridge, the light agent with the playbook achieves 66.7% success, compared with 41.7% for the GR00T-only baseline, and outperforms the strong agent without a playbook. The same playbook also benefits the strong agent, which reaches 79.2% success. These results demonstrate the feasibility of harness distillation for robotics: intervention experience can be accumulated, refined through execution, and reused across agents to improve manipulation.

Recently, self-play fine-tuning (SPIN) has been proposed to adapt large language models to downstream applications with scarce expert-annotated data, by iteratively generating synthetic responses from the model itself. However, SPIN is designed to optimize the current reward advantages of annotated responses over synthetic responses at hand, which may gradually vanish during iterations, leading to unstable optimization. Moreover, the utilization of reference policy induces a misalignment issue between the reward formulation for training and the metric for generation. To address these limitations, we propose a novel Triplet-based Self-Play fIne-tuNing (T-SPIN) method that integrates two key designs. First, beyond current advantages, T-SPIN additionally incorporates historical advantages between iteratively generated responses and proto-synthetic responses produced by the initial policy. Even if the current advantages diminish, historical advantages remain effective, stabilizing the overall optimization. Second, T-SPIN introduces the entropy constraint into the self-play framework, which is theoretically justified to support reference-free fine-tuning, eliminating the training-generation discrepancy. Empirical results on various tasks demonstrate not only the superior performance of T-SPIN over SPIN, but also its stable evolution during iterations. Remarkably, compared to supervised fine-tuning, T-SPIN achieves comparable or even better performance with only 25% samples, highlighting its effectiveness when faced with scarce annotated data.

To make AI systems broadly useful for challenging real-world tasks, we need them to learn complex human goals and preferences. One approach to specifying complex goals asks humans to judge during training which agent behaviors are safe and useful, but this approach can fail if the task is too complicated for a human to directly judge. To help address this concern, we propose training agents via self play on a zero sum debate game. Given a question or proposed action, two agents take turns making short statements up to a limit, then a human judges which of the agents gave the most true, useful information. In an analogy to complexity theory, debate with optimal play can answer any question in PSPACE given polynomial time judges (direct judging answers only NP questions). In practice, whether debate works involves empirical questions about humans and the tasks we want AIs to perform, plus theoretical questions about the meaning of AI alignment. We report results on an initial MNIST experiment where agents compete to convince a sparse classifier, boosting the classifier's accuracy from 59.4% to 88.9% given 6 pixels and from 48.2% to 85.2% given 4 pixels. Finally, we discuss theoretical and practical aspects of the debate model, focusing on potential weaknesses as the model scales up, and we propose future human and computer experiments to test these properties.

Through multi-agent competition, the simple objective of hide-and-seek, and standard reinforcement learning algorithms at scale, we find that agents create a self-supervised autocurriculum inducing multiple distinct rounds of emergent strategy, many of which require sophisticated tool use and coordination. We find clear evidence of six emergent phases in agent strategy in our environment, each of which creates a new pressure for the opposing team to adapt; for instance, agents learn to build multi-object shelters using moveable boxes which in turn leads to agents discovering that they can overcome obstacles using ramps. We further provide evidence that multi-agent competition may scale better with increasing environment complexity and leads to behavior that centers around far more human-relevant skills than other self-supervised reinforcement learning methods such as intrinsic motivation. Finally, we propose transfer and fine-tuning as a way to quantitatively evaluate targeted capabilities, and we compare hide-and-seek agents to both intrinsic motivation and random initialization baselines in a suite of domain-specific intelligence tests.

People are remarkably capable of generating their own goals, beginning with child's play and continuing into adulthood. Despite considerable empirical and computational work on goals and goal-oriented behavior, models are still far from capturing the richness of everyday human goals. Here, we bridge this gap by collecting a dataset of human-generated playful goals (in the form of scorable, single-player games), modeling them as reward-producing programs, and generating novel human-like goals through program synthesis. Reward-producing programs capture the rich semantics of goals through symbolic operations that compose, add temporal constraints, and allow for program execution on behavioral traces to evaluate progress. To build a generative model of goals, we learn a fitness function over the infinite set of possible goal programs and sample novel goals with a quality-diversity algorithm. Human evaluators found that model-generated goals, when sampled from partitions of program space occupied by human examples, were indistinguishable from human-created games. We also discovered that our model's internal fitness scores predict games that are evaluated as more fun to play and more human-like.

We explore the self-play training procedure of large language models (LLMs) in a two-player adversarial language game called Adversarial Taboo. In this game, an attacker and a defender communicate around a target word only visible to the attacker. The attacker aims to induce the defender to speak the target word unconsciously, while the defender tries to infer the target word from the attacker's utterances. To win the game, both players should have sufficient knowledge about the target word and high-level reasoning ability to infer and express in this information-reserved conversation. Hence, we are curious about whether LLMs' reasoning ability can be further enhanced by self-play in this adversarial language game (SPAG). With this goal, we select several open-source LLMs and let each act as the attacker and play with a copy of itself as the defender on an extensive range of target words. Through reinforcement learning on the game outcomes, we observe that the LLMs' performances uniformly improve on a broad range of reasoning benchmarks. Furthermore, iteratively adopting this self-play process can continuously promote LLMs' reasoning abilities. The code is at https://github.com/Linear95/SPAG.

Reinforcement learning with verifiable rewards has become a scalable post-training paradigm for large language models. However, training agents over long-horizon interactions presents two challenges: using only terminal rewards makes turn-level credit assignment sparse and high-variance, while sequential mini-batch updates on a fixed rollout batch introduce policy staleness as the current policy drifts from the behavior policy. Existing approaches obtain denser credit via learned critics, process reward models, or on-policy distillation, but they rely on a value network, step-level annotations, or a stronger external teacher that increase training complexity. Meanwhile, importance sampling and clipping mitigate policy drift, but they do not specify a finite target that stops sequential updates from overshooting. In this work, we introduce TreeOPSD, a critic-free, tree-aware posterior self-distillation framework for long-horizon agentic reinforcement learning. Treating each interaction turn as a tree node, TreeOPSD branches alternative continuations from shared prefixes and recursively backs up terminal rewards into implicit turn-level credit. It then maps each credit to a closed-form, bounded teacher distribution parameterized by the likelihood ratio relative to the frozen behavior policy. Minimizing the divergence between this teacher and the student policy recovers the policy-gradient direction as the tangent at the behavior policy while bounding updates toward a finite target across sequential mini-batches. Empirically, TreeOPSD improves agentic capabilities across several competitive benchmarks and model scales, especially for long-horizon tasks, e.g., raising the average accuracy of Qwen3-30B-A3B-Thinking-2507 by 4.97 points over GRPO on the Deep Research setting.