Blame for scripts/exp02_cs_coverage.py

#!/usr/bin/env python3
"""exp02_cs_coverage -- empirical anytime-valid coverage of the lifted welfare
confidence sequence (Claim 1 / Theorem 4.1) and the fixed-policy corollary
(specs/exp02_cs_coverage.md). No dataset (paper is fully simulated).
"""

import argparse
import json
import math
import os
import sys
import time

sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))

import numpy as np

from core import cs
from core.instance import gini_w, make_instance
from core.oracles import oracle
from core.parallel import run_grid
from core.rounding import dependent_round
from core.swf import swf

ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
RESULTS_PATH = os.path.join(ROOT, "results", "exp02.json")

SEED_BASE = 10_000
N = 20  # instance size (spec: reduced from paper's 50; theorem is n-agnostic)
TOL = 1e-9

# Must match gates.py EXP02_GRID / EXP02_KS / EXP02_DELTAS exactly.
FULL_GRID = [("wpm", "-inf"), ("wpm", -2.0), ("wpm", 0.0), ("wpm", 1.0),
             ("kolm", "-inf"), ("kolm", -2.0), ("kolm", 0.0), ("gini", None)]
FULL_KS = [1, 5, 10]
FULL_DELTAS = [0.1, 0.25]

R_CANDIDATES_FULL = [2000, 1000, 500]
WALL_BUDGET_SEC = 3 * 3600


def log(msg):
    print(f"[exp02] {msg}", file=sys.stderr, flush=True)


def qlabel(q):
    if q is None:
        return None
    if isinstance(q, str):
        return q
    return float(q)


def make_t_grid(T, n_points):
    pts = np.unique(np.round(np.geomspace(1, T, n_points)).astype(int))
    pts = pts[(pts >= 1) & (pts <= T)]
    if pts[0] != 1:
        pts = np.concatenate(([1], pts))
    if pts[-1] != T:
        pts = np.concatenate((pts, [T]))
    return sorted(int(t) for t in np.unique(pts))


# ------------------------------------------------------------- simulation

def simulate_replicate(mu, alpha, beta, w, family, q, k, p_star, W_star, T, delta, seed, t_grid):
    n = len(mu)
    rng = np.random.default_rng(seed)
    init_rounds = math.ceil(n / k)
    p_fix = np.full(n, k / n)
    W_fix_true = swf(mu * p_fix, family, w, q)

    mu_up = np.full(n, cs.U_MAX)
    mu_low = np.full(n, cs.U_MIN)
    N_i = np.zeros(n)
    mu_hat = np.zeros(n)

    L = len(t_grid)
    pointwise_miss = np.zeros(L, dtype=bool)
    running_missed = np.zeros(L, dtype=bool)
    width_at_grid = np.zeros(L, dtype=float)
    gi = 0

    missed_so_far = False
    link_ever_bad = {"i": False, "ii": False, "iii": False, "iv": False}
    fixed_ever_bad = False

    for t in range(1, T + 1):
        p_up_t = oracle(mu_up, family, w, q, k)
        p_low_t = oracle(mu_low, family, w, q, k)
        W_up_t = swf(mu_up * p_up_t, family, w, q)
        W_low_t = swf(mu_low * p_low_t, family, w, q)
        covered_t = (W_low_t <= W_star + TOL) and (W_up_t >= W_star - TOL)
        if not covered_t:
            missed_so_far = True

        swf_mu_p_low = swf(mu * p_low_t, family, w, q)
        swf_muup_p_star = swf(mu_up * p_star, family, w, q)
        if not (W_star >= swf_mu_p_low - TOL):
            link_ever_bad["i"] = True
        if not (swf_mu_p_low >= W_low_t - TOL):
            link_ever_bad["ii"] = True
        if not (swf_muup_p_star >= W_star - TOL):
            link_ever_bad["iii"] = True
        if not (W_up_t >= swf_muup_p_star - TOL):
            link_ever_bad["iv"] = True

        W_fix_low = swf(mu_low * p_fix, family, w, q)
        W_fix_up = swf(mu_up * p_fix, family, w, q)
        if not (W_fix_low <= W_fix_true + TOL and W_fix_up >= W_fix_true - TOL):
            fixed_ever_bad = True

        if gi < L and t == t_grid[gi]:
            pointwise_miss[gi] = not covered_t
            running_missed[gi] = missed_so_far
            width_at_grid[gi] = W_up_t - W_low_t
            gi += 1

        if t <= init_rounds:
            idx = [((t - 1) * k + j) % n for j in range(k)]
            S_t = np.array(idx, dtype=int)
        else:
            S_t = np.nonzero(dependent_round(p_up_t, rng))[0]

        for i in S_t:
            N_old = N_i[i]
            u_ti = 0.1 + 0.9 * rng.beta(alpha[i], beta[i])
            mu_hat[i] = (N_old * mu_hat[i] + u_ti) / (N_old + 1.0)
            N_i[i] = N_old + 1.0
            mu_up[i] = float(np.clip(cs.update_up(mu_hat[i], N_old, n, delta), cs.U_MIN, cs.U_MAX))
            mu_low[i] = float(np.clip(cs.update_low(mu_hat[i], N_old, n, delta), cs.U_MIN, cs.U_MAX))

    return dict(
        any_miss=missed_so_far,
        pointwise_miss=pointwise_miss,
        running_missed=running_missed,
        width_at_grid=width_at_grid,
        link_ever_bad=link_ever_bad,
        fixed_ever_bad=fixed_ever_bad,
    )


def simulate_chunk(mu, alpha, beta, w, family, q, k, p_star, W_star, T, delta, seeds, t_grid):
    L = len(t_grid)
    sum_any_miss = 0
    sum_pointwise = np.zeros(L)
    sum_running = np.zeros(L)
    sum_width = np.zeros(L)
    sum_link = {"i": 0, "ii": 0, "iii": 0, "iv": 0}
    sum_fixed = 0
    for seed in seeds:
        res = simulate_replicate(mu, alpha, beta, w, family, q, k, p_star, W_star, T, delta, seed, t_grid)
        sum_any_miss += int(res["any_miss"])
        sum_pointwise += res["pointwise_miss"]
        sum_running += res["running_missed"]
        sum_width += res["width_at_grid"]
        for key in sum_link:
            sum_link[key] += int(res["link_ever_bad"][key])
        sum_fixed += int(res["fixed_ever_bad"])
    return dict(n=len(seeds), sum_any_miss=sum_any_miss, sum_pointwise=sum_pointwise.tolist(),
                sum_running=sum_running.tolist(), sum_width=sum_width.tolist(),
                sum_link=sum_link, sum_fixed=sum_fixed)


def combine_chunks(chunk_results, t_grid, family, q, k, delta, W_star):
    R = sum(c["n"] for c in chunk_results)
    sum_any_miss = sum(c["sum_any_miss"] for c in chunk_results)
    sum_pointwise = np.sum([c["sum_pointwise"] for c in chunk_results], axis=0)
    sum_running = np.sum([c["sum_running"] for c in chunk_results], axis=0)
    sum_width = np.sum([c["sum_width"] for c in chunk_results], axis=0)
    sum_link = {key: sum(c["sum_link"][key] for c in chunk_results) for key in ("i", "ii", "iii", "iv")}
    sum_fixed = sum(c["sum_fixed"] for c in chunk_results)

    anytime_miss_rate = sum_any_miss / R
    anytime_miss_se = math.sqrt(anytime_miss_rate * (1.0 - anytime_miss_rate) / R)
    pointwise_miss_rate = (sum_pointwise / R).tolist()
    running_miss_rate = (sum_running / R).tolist()
    mean_width = (sum_width / R).tolist()
    link_miss_rates = {key: sum_link[key] / R for key in sum_link}
    fixed_policy_anytime_miss_rate = sum_fixed / R

    t_arr = np.array(t_grid, dtype=float)
    mw_arr = np.array(mean_width, dtype=float)
    last_decade = t_arr >= (t_arr[-1] / 10.0)
    if last_decade.sum() < 2:
        last_decade = np.ones_like(t_arr, dtype=bool)
    slope, _ = np.polyfit(np.log(t_arr[last_decade]), np.log(np.maximum(mw_arr[last_decade], 1e-300)), 1)

    return {
        "family": family, "q": qlabel(q), "k": k, "delta": delta, "R": R,
        "anytime_miss_rate": anytime_miss_rate, "anytime_miss_se": anytime_miss_se,
        "running_miss_rate": running_miss_rate,
        "pointwise_miss_rate": pointwise_miss_rate,
        "link_miss_rates": link_miss_rates,
        "fixed_policy_anytime_miss_rate": fixed_policy_anytime_miss_rate,
        "mean_width": mean_width,
        "width_decay_alpha": float(slope),
        "W_star": float(W_star),
    }


# --------------------------------------------------------------- grid setup

def build_cells(toy):
    if toy:
        combos = [("wpm", "-inf"), ("wpm", 0.0), ("kolm", -2.0), ("gini", None)]
        ks, deltas = [1, 5], [0.1]
        T, R, n_grid_points, chunk_size = 60, 25, 8, 10
    else:
        combos = FULL_GRID
        ks, deltas = FULL_KS, FULL_DELTAS
        T, R, n_grid_points, chunk_size = 2000, 2000, 40, 50
    cells = [(f, q, k, d) for f, q in combos for k in ks for d in deltas]
    return cells, T, R, n_grid_points, chunk_size


def calibrate_and_pick_R(mu, alpha, beta, pstar_cache, cells_spec, T, n_jobs, candidates):
    T_probe = 100
    probe_grid = make_t_grid(T_probe, 5)
    combos = sorted(set((f, qlabel(q), k) for f, q, k, d in cells_spec),
                     key=lambda c: (c[0], str(c[1]), c[2]))
    step_time = {}
    for family, qk, k in combos:
        q_actual = next(q for f, q, kk, d in cells_spec if f == family and qlabel(q) == qk and kk == k)
        p_star, W_star, w_eff = pstar_cache[(family, qk, k)]
        t0 = time.time()
        simulate_replicate(mu, alpha, beta, w_eff, family, q_actual, k, p_star, W_star,
                            T_probe, 0.1, 999_999, probe_grid)
        dt = (time.time() - t0) / T_probe
        step_time[(family, qk, k)] = dt
        log(f"calibration family={family} q={qk} k={k}: {dt * 1e6:.2f} us/step")

    total_step_time = sum(step_time[(f, qlabel(q), k)] for f, q, k, d in cells_spec)
    note = None
    chosen = candidates[-1]
    for R_cand in candidates:
        projected = total_step_time * T * R_cand / n_jobs
        log(f"projected wall time for R={R_cand}: {projected / 3600:.2f} h")
        if projected <= WALL_BUDGET_SEC:
            chosen = R_cand
            if R_cand < candidates[0]:
                note = (f"R reduced from {candidates[0]} to {R_cand}: projected wall time at "
                        f"R={candidates[0]} exceeded the {WALL_BUDGET_SEC / 3600:.0f}h budget")
            break
    else:
        chosen = candidates[-1]
        projected = total_step_time * T * chosen / n_jobs
        note = (f"R reduced to floor {chosen}; projected wall time still "
                f"{projected / 3600:.2f}h, exceeds {WALL_BUDGET_SEC / 3600:.0f}h budget")
    return chosen, note


def main():
    ap = argparse.ArgumentParser()
    ap.add_argument("--toy", action="store_true")
    args = ap.parse_args()
    t0 = time.time()

    n_jobs = max(1, min(int(os.environ.get("JOB_CORES", "4")), 12))
    log(f"JOB_CORES(n_jobs)={n_jobs} numpy={np.__version__} toy={args.toy}")

    instance = make_instance(n=N, weight_decay="exp", seed=0)
    mu, alpha, beta, w = instance["mu"], instance["alpha"], instance["beta"], instance["w"]
    log(f"instance built: n={N}, mu[:5]={np.round(mu[:5], 4).tolist()}")

    cells_spec, T, R, n_grid_points, chunk_size = build_cells(args.toy)
    t_grid = make_t_grid(T, n_grid_points)
    log(f"cells={len(cells_spec)} T={T} R={R} t_grid: {len(t_grid)} points "
        f"[{t_grid[0]}..{t_grid[-1]}]")

    pstar_cache = {}
    for family, q, k, delta in cells_spec:
        key = (family, qlabel(q), k)
        if key in pstar_cache:
            continue
        w_eff = gini_w(w, instance["weight_decay"]) if family == "gini" else w
        p_star = oracle(mu, family, w_eff, q, k)
        W_star = swf(mu * p_star, family, w_eff, q)
        pstar_cache[key] = (p_star, W_star, w_eff)
    log(f"precomputed p_star/W_star for {len(pstar_cache)} (family,q,k) combos")

    R_used, R_note = R, None
    if not args.toy:
        R_used, R_note = calibrate_and_pick_R(mu, alpha, beta, pstar_cache, cells_spec, T, n_jobs,
                                               R_CANDIDATES_FULL)
    log(f"replicates per cell: R={R_used}" + (f" ({R_note})" if R_note else ""))

    tasks = []
    for cell_idx, (family, q, k, delta) in enumerate(cells_spec):
        key = (family, qlabel(q), k)
        p_star, W_star, w_eff = pstar_cache[key]
        seeds_all = [SEED_BASE + r for r in range(R_used)]
        for start in range(0, R_used, chunk_size):
            chunk_seeds = seeds_all[start:start + chunk_size]
            tasks.append((cell_idx, family, q, k, delta, p_star, W_star, w_eff, T, chunk_seeds))
    log(f"built {len(tasks)} chunk tasks across {len(cells_spec)} cells (chunk_size={chunk_size})")

    def _run_chunk_task(task):
        cell_idx, family, q, k, delta, p_star, W_star, w_eff, T_, seeds = task
        res = simulate_chunk(mu, alpha, beta, w_eff, family, q, k, p_star, W_star, T_, delta, seeds, t_grid)
        return cell_idx, res

    t_sim0 = time.time()
    raw_results = run_grid(_run_chunk_task, tasks, n_jobs=n_jobs)
    log(f"all {len(raw_results)} chunk tasks completed in {time.time() - t_sim0:.1f}s")

    by_cell = {i: [] for i in range(len(cells_spec))}
    for cell_idx, chunk_res in raw_results:
        by_cell[cell_idx].append(chunk_res)

    cells_out = []
    for cell_idx, (family, q, k, delta) in enumerate(cells_spec):
        _, W_star, _ = pstar_cache[(family, qlabel(q), k)]
        cell_out = combine_chunks(by_cell[cell_idx], t_grid, family, q, k, delta, W_star)
        cells_out.append(cell_out)
        log(f"cell family={family} q={q} k={k} delta={delta}: "
            f"anytime_miss={cell_out['anytime_miss_rate']:.4f} se={cell_out['anytime_miss_se']:.4f} "
            f"alpha={cell_out['width_decay_alpha']:.3f}")

    max_anytime = max((c["anytime_miss_rate"] for c in cells_out), default=0.0)
    n_exceed_delta = sum(1 for c in cells_out if c["anytime_miss_rate"] > c["delta"])
    n_exceed_delta_3se = sum(1 for c in cells_out
                              if c["anytime_miss_rate"] > c["delta"] + 3 * c["anytime_miss_se"])

    meta = dict(
        exp="exp02", n_cores_used=n_jobs, wall_time_sec=time.time() - t0,
        seed_base=SEED_BASE, numpy_version=np.__version__, n=N, T=T, R=R_used,
        ambiguities={"beta_prior": "U[1,5] seed 0", "mu_up_init": 1.0, "mu_low_init": 0.1,
                     "clip_range": [0.1, 1.0], "init_rule": "round_robin"},
    )
    if R_note:
        meta["R_reduction_note"] = R_note

    out = dict(
        meta=meta,
        status="ok",
        t_grid=t_grid,
        cells=cells_out,
        summary=dict(n_cells=len(cells_out), max_anytime_miss_rate=max_anytime,
                     n_cells_exceeding_delta=n_exceed_delta,
                     n_cells_exceeding_delta_plus_3se=n_exceed_delta_3se),
    )

    os.makedirs(os.path.dirname(RESULTS_PATH), exist_ok=True)
    with open(RESULTS_PATH, "w") as fh:
        json.dump(out, fh, indent=2)

    elapsed = time.time() - t0
    print(f"exp02 done in {elapsed:.1f}s (toy={args.toy}, n_jobs={n_jobs}, R={R_used})")
    print(f"cells: {len(cells_out)}, max_anytime_miss_rate={max_anytime:.4f}")
    print(f"n_cells_exceeding_delta={n_exceed_delta}, n_cells_exceeding_delta_plus_3se={n_exceed_delta_3se}")
    print(f"results written to {RESULTS_PATH}")
    return 0


if __name__ == "__main__":
    sys.exit(main())