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| #!/usr/bin/env python3 | |
| from __future__ import annotations | |
| import json | |
| import math | |
| import sys | |
| from pathlib import Path | |
| def independent_bound(row: dict) -> float: | |
| eigenvalues = row["prior_eigenvalues"] | |
| d = row["d"] | |
| horizon = row["T"] | |
| q = 24.0 * math.log(horizon) / d | |
| c1 = math.sqrt(1.0 + max(q, math.sqrt(q))) | |
| c2 = 2.0 * c1 * math.sqrt(math.log(1.0 + row["radius"] ** 2 * max(eigenvalues) * horizon / (d * row["sigma"] ** 2))) | |
| return ( | |
| d * row["sigma"] * math.sqrt(horizon) * c2 | |
| + 3.0 * math.sqrt(2.0) * row["radius"] * math.sqrt(d) * sum(math.sqrt(value) for value in eigenvalues) * c1 | |
| + math.sqrt(2.0 * row["radius"] ** 2 * sum(eigenvalues)) | |
| ) | |
| def main() -> None: | |
| evidence = json.loads(Path(sys.argv[1]).read_text()) | |
| rows = evidence["rows"] | |
| relative_errors = [abs(independent_bound(row) - row["theorem_1_bound"]) / row["theorem_1_bound"] for row in rows] | |
| checks = { | |
| "all_covariance_eigenvalues_positive": all(min(row["prior_eigenvalues"]) > 0 for row in rows), | |
| "all_actions_use_positive_radius": all(row["radius"] > 0 for row in rows), | |
| "formula_reconstruction_matches": max(relative_errors) < 1e-12, | |
| "confidence_intervals_finite": all(math.isfinite(row["regret_ci95_low"]) and math.isfinite(row["regret_ci95_high"]) for row in rows), | |
| "legacy_column_has_exact_sqrt_T_multiplier": all(abs(row["legacy_multiplicative_burnin_scale"] / row["corollary_burnin_scale"] - math.sqrt(row["T"])) < 1e-12 for row in rows), | |
| } | |
| output = {"passed": all(checks.values()), "checks": checks, "max_formula_relative_error": max(relative_errors)} | |
| print(json.dumps(output, sort_keys=True)) | |
| raise SystemExit(0 if output["passed"] else 1) | |
| if __name__ == "__main__": | |
| main() | |