Эксперимент: Cross-Partial Nash Compatibility Regularizer (#465)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified an autograd cross-partial compatibility regularizer for a two-agent centralized-critic toy problem. The autograd residual matched an independent finite-difference calculation to 2.0e-12; the residual followed the predicted 2/(1+4λ) law across the lambda sweep, and the Gibbs incompatibility squared followed the predicted 1/γ² law exactly. Regularization reduced the residual from 2.0 to 0.4 at λ=1, while critic fitting loss increased from approximately 0 to 0.64 because the deliberately incompatible target critics cannot both be preserved under a conservative-field constraint; this confirms the mechanism, but not an RL return improvement.", "metrics": { "baseline": "lambda=0: absolute cross-partial residual 2.0000; critic fit loss 1.87e-18", "idea": "lambda=1: absolute cross-partial residual 0.4000; critic fit loss 0.6400; predicted residual 0.4000", "finite_difference_check": "Autograd residual 2.000000000000 versus finite-difference residual 2.000000000002; absolute error 2.0e-12", "lambda_prediction": "Observed relative error at most 1.4e-9 for lambda in {0, 0.05, 0.25, 0.5, 1, 2, 5}", "gamma_prediction": "Observed squared Gibbs mismatch exactly matched 4/gamma^2 for gamma in {0.25, 0.5, 1, 2, 4}" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a controlled two-agent scalar-action critic-fitting MVP, not a full MADDPG, MASAC, or environment experiment. It does not measure environment return, actor-gradient variance, replay-buffer sample efficiency, Hutchinson estimation, or wall-clock overhead in a high-dimensional neural critic." }