Эксперимент: Drift-Balanced Adaptive Constraint Multiplier (#925)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible projected dual-multiplier controller in a small stochastic policy/violation dynamical system. The mechanism manifested: projection error was exactly 0, interior drift identity error was 4.5e-17, cap-hit steps matched the predicted ceil(lambda_max/(alpha*(v-tau))) at all four tested alphas, and stable runs converged to mean violation 0.2. In the noisy sweep, multiplier standard deviation increased from 0.0072 at alpha=0.01 to 1.2268 at alpha=6.4, with cap contact appearing at alpha=6.4; the adaptive controller also had lower target-error than the best fixed-penalty grid point (0.00078 vs 0.01625).", "metrics": { "baseline": "Best fixed penalty from 21-point grid: penalty=1.0, tail mean violation=0.21625, absolute target error=0.01625.", "idea": "Adaptive alpha=0.08: tail mean violation=0.20078, absolute target error=0.00078, mean lambda=1.0135. Deterministic drift balance gave target error <=7.6e-7 for alpha in {0.01,0.05,0.1,0.2,0.4}. Constant-error cap scaling observed/predicted steps: alpha=.02 143/143, .05 58/58, .1 29/29, .2 15/15. Noisy lambda std for alpha=.01/.1/.8/1.6/3.2/6.4: .0072/.0280/.1321/.2814/.6240/1.2268." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py && /home/maxwelhelp/main/bin/python3 noisy_sweep.py", "files": [ "experiment.py", "noisy_sweep.py", "results.json", "noisy_sweep.json" ], "limitations": "This is a toy scalar policy-response model with Bernoulli terminal violations, not a full PPO/GRPO two-dimensional navigation implementation. It does not test neural-network optimization, trajectory returns/group normalization, wall-clock speed, or robustness across random seeds; the fixed-penalty baseline was selected by an oracle grid sweep." }