Эксперимент: Bellman Stopping Controller for Self-Refinement (#780)

{ "worked": true, "confidence": 9, "verdict": "Built an exact finite-horizon Bellman stopping controller for a stochastic score-refinement environment, with Monte Carlo comparison against fixed 1/3/5-step budgets. The mechanism manifested: continuation decreased monotonically with cost, the stop region was an upper score threshold that moved from 0.60 at cost 0.02 to 0.10 at cost 0.04, and all Bellman residuals were 0. At cost 0.038, adaptive stopping used 3.626 calls versus 5 fixed calls while achieving objective 0.00947 versus 0.00690 for fixed-5; this is a promising toy signal, not evidence of real-model improvement.", "metrics": { "baseline": "At cost 0.038: fixed-1 = 1.000 calls, quality 0.04245, objective 0.00445; fixed-3 = 3.000 calls, quality 0.12281, objective 0.00881; fixed-5 = 5.000 calls, quality 0.19690, objective 0.00690.", "idea": "At cost 0.038: adaptive = 3.626 calls, quality 0.14726, objective 0.00947. Exact Bellman residual = 0.0 and Delta>cost decisions matched the policy for every tested state. Cost sweep calls: 5.00 at 0.02, 4.60 at 0.035, 3.62 at 0.038, 2.40 at 0.04, and 0 at 0.045." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 bellman_stopping_experiment.py", "files": [ "bellman_stopping_experiment.py", "results.json", "run_output.txt" ], "limitations": "Only a synthetic one-dimensional score environment with known transitions and payoff was tested. The continuation value was computed exactly rather than learned from logged verifier/model trajectories; no LLM, HumanEval/MBPP, calibrated verifier, embedding state, wall-clock measurement, or GPU experiment was tested." }