# Эксперимент: Bellman-Resolvent Uncertainty Targets (#499)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a readable finite-state Bellman-resolvent uncertainty prototype with bootstrap one-step variance, discounted transition propagation, uncertainty-weighted fitted value iteration, and saved numerical results. The gain sweep matched 1/(1-gamma*lambda) to floating-point precision, truncation residual matched (gamma*lambda)^K/(1-gamma*lambda), the gamma*lambda>1 boundary showed explosive growth, and the propagated Gaussian variance matched within 0.014%. In the matched offline toy experiment, resolvent weighting reduced value RMSE from 1.8461 to 1.6026 (-13.2%), Bellman RMSE from 0.1285 to 0.1244 (-3.1%), and late-state RMSE from 2.2479 to 1.9511 (-13.2%); this is promising but only a small synthetic result.",
  "metrics": {
    "baseline": "Toy mechanism: exact predicted gain/truncation formulas; offline value RMSE 1.846088, Bellman RMSE 0.1284779, late-state RMSE 2.247931",
    "idea": "Toy mechanism: relative errors approximately 0 to 1e-13; variance relative error 0.000138; offline value RMSE 1.602595, Bellman RMSE 0.1244343, late-state RMSE 1.951077; uncertainty-error correlation 0.61067"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Not tested on CartPole, SAC/DQN, neural networks, real offline RL datasets, multiple random seeds, policy improvement, calibration metrics beyond correlation, or computational overhead. The finite-state toy uses known transition dynamics for propagation and a diagonal one-step variance approximation."
}