Эксперимент: Recursive Bellman Variance Targets (#383)

{ "worked": true, "confidence": 9, "verdict": "Built a finite-horizon stochastic-tree verifier implementing recursive Bellman mean/variance propagation plus a small heteroscedastic regression comparison. The mechanism manifested: recursive variance matched Monte Carlo variance within 0.56% across horizons, the transition-selection term exactly followed p(1-p)Δ² and vanished at deterministic transitions, and horizon variance matched predicted discounted accumulation under both deterministic and random transitions. The neural mini-experiment did not show a performance win: MSE was 0.24654 baseline versus 0.24735 for the idea, with essentially identical calibration ratios.", "metrics": { "baseline": "Tiny regression: test MSE 0.24654; calibration ratio E[(y-v)^2/q] = 0.27029.", "idea": "Tiny recursive-variance-weighted regression: test MSE 0.24735; calibration ratio = 0.27076. Mechanism checks: recursion-vs-Monte-Carlo relative error 0.00002-0.00558; selection term exact over p=0..1; horizon MC/prediction agreement within about 0.5%." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 verify.py", "files": [ "verify.py", "results.json", "run_output.txt" ], "limitations": "This is a controlled toy stochastic process, not CartPole or a trained RL/world-model agent. It uses known transition and reward statistics, does not test learned child variance error, nonzero reward/return covariance, rollout allocation, branch counts 1/2/4/8/16, or compute/FLOP efficiency; the baseline comparison is only a small supervised regression rather than an end-to-end Bellman learner." }