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| <h1>KL-regularized bandit theory: exact claim audit</h1> | |
| <div class="meta">ICML 2026 paper 20430 · OpenReview XarOZG8Un0 · arXiv 2603.02155</div> | |
| <div class="banner"><strong>Truth over points:</strong> two upper rates survive corrected constants; both lower theorems fail over their literal parameter domains.</div> | |
| <section class="grid"> | |
| <article class="card"><h2>Claim 1 · <span class="status verified">VERIFIED + CORRECTED</span></h2><p>3,240 optimistic-gap fixtures and 3,279 exhaustive count paths support the fast <code>O~(ηK log²T)</code> rate. A factor-two typo and a false equality are disclosed and repaired.</p></article> | |
| <article class="card"><h2>Claim 2 · <span class="status verified">VERIFIED + CORRECTED</span></h2><p>The source miscomputes an integral. The valid <code>2√KT</code> count bound passes 29,523 paths and preserves the eta-independent slow rate.</p></article> | |
| <article class="card"><h2>Claim 3 · <span class="status falsified">FALSIFIED AS STATED</span></h2><p>Playing the reference policy costs at most <code>ηT/8</code>. At <code>T=K, η=1/K</code>, this is <code>1/8</code> while the asserted lower scale is <code>2 log K</code>. The paper's means also leave <code>[0,1]</code>.</p></article> | |
| <article class="card"><h2>Claim 4 · <span class="status falsified">FALSIFIED AS STATED</span></h2><p>At <code>T=1, η=log(K)/√K</code>, a universal upper bound contradicts <code>Ω(√KT)</code>. With <code>T≥8K</code>, corrected separation and KL constants repair the intended rate.</p></article> | |
| <article class="card wide"><h2>Claim 5 · <span class="status verified">VERIFIED</span></h2><p>The exact bonus and Freedman mean/variance conditions pass. Across 5,000 adaptive trials the full bonus fails at rate <code>0.0022</code>; removing the simultaneous <code>log(TK)</code> factor raises failure to <code>0.5822</code>.</p></article> | |
| <article class="card wide"><h2>Reproducibility</h2><table><tr><th>Route</th><th>Scale</th><th>Compute</th></tr><tr><td>Exact proof/algebra audit</td><td>all 5 claims; 32,802 exhaustive paths</td><td>Python standard library, local CPU</td></tr><tr><td>Adaptive coverage + control</td><td>5,000 fixed-seed trials</td><td>3.4 s total, $0, no GPU</td></tr><tr><td>Independent verifier</td><td>frozen SHA + counterfamily invariants</td><td>all checks pass</td></tr></table></article> | |
| </section> | |
| <footer>Evidence: <a href="https://github.com/MachineLearning-Nerd/XarOZG8Un0">GitHub</a> · Logbook: <a href="https://huggingface.co/spaces/DineshAI/XarOZG8Un0">Hugging Face</a> · Source: <a href="https://arxiv.org/abs/2603.02155">arXiv 2603.02155</a></footer> | |
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