scripts/claim5_supplement.py

"""CLAIM 5, supplement -- the d-exponent measured at a FIXED aspect ratio T/d.

In the main script d is swept at a fixed horizon T = 4000, so T/d falls from 1000 to 125 and
the envelope/sqrt(dT) ratio drifts upward (0.54 -> 0.80); the fitted d-exponent (0.69) is
biased by that drift.  Theorem 5.2 assumes T >= 4d, and sqrt(dT) is the rate in the regime
T >> d.  Sweeping d with T = 500 d holds the aspect ratio fixed, and then sqrt(dT) = sqrt(500)*d,
so the predicted exponent in d is 1.
"""

from __future__ import annotations

import json
import os
import sys

import numpy as np

sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
from batch import fit_exponent
from claim5_lowerbound import ALGS, SEED, theorem_floor


def main(seeds=12):
    rows = []
    for d in [4, 8, 16, 32]:
        T = 500 * d
        sigma = 1.0 / np.sqrt(2 * d)
        env = np.inf
        per = {}
        for name, fn in ALGS.items():
            worst = -np.inf
            for c in [0.5, 1.0, 2.0]:
                Delta = c / np.sqrt(T)
                vals = []
                for s in range(seeds):
                    rng = np.random.default_rng(SEED + 31 * s + d + int(10 * c))
                    theta = (rng.integers(2, size=d) * 2.0 - 1.0) * Delta
                    vals.append(fn(T, d, theta, sigma, rng))
                worst = max(worst, float(np.mean(vals)))
            per[name] = worst
            env = min(env, worst)
        rows.append(
            dict(
                d=d,
                T=T,
                aspect_ratio=T / d,
                per_algorithm=per,
                empirical_minimax_envelope=env,
                sqrt_dT=float(np.sqrt(d * T)),
                envelope_over_sqrt_dT=env / float(np.sqrt(d * T)),
                theorem_floor=float(theorem_floor(d, T)),
                above_theorem_floor=bool(env >= theorem_floor(d, T)),
            )
        )
    sl, _, se = fit_exponent(
        [r["d"] for r in rows], [r["empirical_minimax_envelope"] for r in rows]
    )
    res = dict(
        claim="claim-5 supplement: d-exponent at fixed aspect ratio T = 500 d",
        seed=SEED,
        seeds=seeds,
        rows=rows,
        fitted_d_exponent=sl,
        stderr=se,
        predicted=1.0,
        note="at T = 500 d, sqrt(dT) = sqrt(500) d, so a sqrt(dT) rate shows up as a "
        "d-exponent of 1",
    )
    out = os.path.join(
        os.path.dirname(os.path.dirname(os.path.abspath(__file__))),
        "outputs",
        "claim5_supplement.json",
    )
    with open(out, "w") as f:
        json.dump(res, f, indent=1)
    print(json.dumps(res, indent=1))


if __name__ == "__main__":
    main()