Adaptive Barrier-Margin Regularization MVP

Implementation

experiment.py implements the proposed residual r = kappa * epsilon - psi, a squared softplus penalty, detached disturbance/uncertainty estimates, the clipped adaptive update, and an inference-time projection filter. The toy plant is a scalar bounded point-mass-like control task with Gaussian unmodeled force. Ordinary supervised policy learning, a fixed robust margin, and the adaptive margin use the same policy, data, optimizer, and 700 updates.

Quantitative mechanism checks

Results are in results.json.

1. Adaptive fixed point: for disturbance absolute-error mean e=0.32, delta=0.1, the update predicts epsilon*=e/(1-delta)=0.355556; observed after 100 updates: 0.355556.
2. Convergence factor: with rho=0.25, the linear error factor predicts 1-rho*(1-delta)=0.775; observed: 0.775000.
3. Scaling and coverage: for Gaussian error standard deviation sigma, the update predicts epsilon*=sigma*sqrt(2/pi)/(1-delta), hence epsilon scales linearly with sigma. This is observed (0.04468, 0.08937, 0.17873, 0.35747 for sigma 0.05, 0.1, 0.2, 0.4). However, this mean-error fixed point gives only about 0.624 coverage for a two-sided absolute Gaussian error, not the claimed 0.9 coverage; the empirical coverage sweep in results.json confirms approximately 0.624 at every sigma. The 0.9 quantile itself gives 0.9 coverage, demonstrating the calibration mismatch.

Mini-experiment

Adaptive margins increase with disturbance amplitude and substantially reduce policy/filter intervention compared with baseline (zero intervention in this toy run because the policy learns inside the reconstructed margin). But post-filter violation rises from 0.0003 at sigma 0.05 to 0.1223 at sigma 0.4; adaptive epsilon is below the 90th-percentile error and therefore does not provide the stated 1-delta coverage. The fixed margin has higher tracking MSE (1.077) and becomes less safe at high disturbance (0.204 violation at sigma 0.4), while baseline has about 0.497 violation throughout.

Decision

The adaptive barrier mechanism and its parameter dynamics manifest, but the proposed uncertainty update does not establish the stated coverage guarantee. Therefore this MVP is marked worked=false for the full idea: it is a useful adaptive regularizer signal, not a validated coverage-preserving safety method. A quantile/conformal calibration update would be needed before claiming the safety effect.