# Эксперимент: Barrier-Certified Neural Policy Training (#777)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a differentiable 1D neural-policy CBF trainer and dense certificate-verification sweep. The Lipschitz lower bound held for every net; the residual gap had observed log-log slope 1.0000001 versus predicted 1, with coefficient error below 1.7e-7; and the predicted positive-certificate threshold delta<epsilon/L=0.08 was conservative relative to the observed safe boundary at delta=0.125. Task-only training reached terminal x=-0.448 with minimum residual -0.605, while barrier training reached x=0.097 with minimum residual 0.0807 and dense unseen-state minimum 0.0788, at substantially worse task error.",
  "metrics": {
    "baseline": "terminal x=-0.4481; task error=0.00186; min rollout residual=-0.6049; dense unseen minimum residual=-0.4450; 100% of residual samples below epsilon",
    "idea": "terminal x=0.0972; task error=0.5472; min rollout residual=0.08068; dense unseen minimum residual=0.07881; 0% of residual samples below epsilon",
    "certificate": "L=1, epsilon=0.08, predicted delta threshold=0.08, observed safe boundary=0.125, residual-gap/delta approximately 0.6366197, observed log-log slope=1.0000001"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 barrier_experiment.py",
  "files": [
    "barrier_experiment.py",
    "results.json"
  ],
  "limitations": "This is a tiny 1D integrator toy with h(x)=x and analytically simple dynamics, not a pendulum, Dubins car, learned world model, multidimensional reachable-set certificate, or formal neural-policy Lipschitz bound. The dense unseen-state check covers x in [0,1] only, and training uses one fixed seed and one barrier weight rather than a statistical hyperparameter sweep."
}