Эксперимент: Lyapunov-Certified Policy Training (#1066)

{ "worked": false, "confidence": 9, "verdict": "Built a PyTorch MVP with an equilibrium-preserving policy, positive Lyapunov network, hinge certificate loss, grid verification, radius sweep, and rollout monitoring in experiment.py. The algebraic recurrence V_{t+1}<=qV_t was verified synthetically, and increasing certificate weight reduced sampled violation from 0.934 (lambda=0) to 0.00030 (lambda=4), but the claimed contraction factor q=0.6875 was not observed: certified one-step V ratios were roughly 0.90-0.99. This exposes a limitation in the stated math: V>=c1||x||^2 alone cannot convert decrease proportional to ||x||^2 into geometric decay in V; an upper bound V<=c3||x||^2 is also required. Therefore the practical penalty effect appeared, but the authoritative Lyapunov contraction claim was not confirmed.", "metrics": { "baseline": "lambda_delta=0: task MSE 7.49e-06, mean hinge violation 0.9340, certified fraction 72.9%, certified radius 0.0, rollout V30/V0=1.208", "idea": "lambda_delta=4: task MSE 4.32e-03, mean hinge violation 2.96e-04, certified fraction 99.57%, certified radius 0.35 in the main grid, certified one-step ratio median 0.897 and max 0.978; rollout V30/V0=0.00071" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run4.log" ], "limitations": "Only a tiny 2D deterministic benchmark was tested; no learned dynamics model, transition-model error, held-out generalization, interval certification, PPO/RL training, action rejection monitor, or multiple random seeds was evaluated. The radius sweep has grid-resolution and near-equilibrium numerical sensitivity." }