Certified Stochastic Control via Covariance Steering with Pick-to-Learn

Abstract

We present CS-P2L, a framework coupling covariance steering (CS) with the Pick-to-Learn (P2L) meta-algorithm for certified controller synthesis over high-fidelity stochastic simulators. The method iteratively evaluates policies on simulator rollouts, tightens surrogate constraints using the worst-case violations, and provides compression-based probabilistic guarantees on the true violation probability given a confidence level. On a spacecraft powered-descent problem with uncertain gravity, CS-P2L certifies a violation bound of 4.9\% with 600 rollouts, whereas standalone covariance steering underestimates the violation rate by roughly a factor of two.