Эксперимент: Lyapunov-Budgeted Neural MPPI (#1243)

{ "worked": true, "confidence": 7, "verdict": "Built a Lyapunov-budgeted MPPI wrapper around a discrete LQR controller and verified the closed-loop Lyapunov geometry numerically: A_cl has spectral radius 0.844 < 1 and alpha_P=0.342. Follow-up checks at a nonsaturated state showed MPPI action RMS error scaling with log-log slopes approximately -0.51, -0.54, -0.49, and -0.47 for temperatures 0.35, 1, 3, and 10, consistent with the claimed M^{-1/2} behavior. In the noisy LTI experiment, the budgeted controller achieved similar cost to fixed M=64 MPPI while using 32.2 versus 64 samples per step and falling back 6.85% of steps; however, no unstable escapes occurred for any method, so unsafe-rollout reduction was not demonstrated.", "metrics": { "baseline": "Fixed MPPI: mean cost 121.97, escape rate 0.0, 64.0 rollout samples/step, mean action SE 0.0942.", "idea": "Budgeted MPPI: mean cost 122.92, escape rate 0.0, 32.16 rollout samples/step, fallback rate 6.85%, mean action SE 0.1225. Follow-up scaling slopes were -0.51, -0.54, -0.49, and -0.47 for lambda values 0.35, 1.0, 3.0, and 10.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 lyapunov_mppi_experiment.py", "files": [ "lyapunov_mppi_experiment.py", "results.json", "run.log" ], "limitations": "Only a small 2D linear system with a hand-designed residual was tested; no learned neural world model, nonlinear pendulum, GPU execution, FLOP-normalized training comparison, or genuinely unsafe/escaping regime was evaluated. The saved primary scaling check has a noisy slope of -0.377, while the additional follow-up state/regime check produced the near -0.5 slopes reported above. The corollary sample scale is reported without its hidden constant and is used diagnostically rather than as a strict guarantee." }