VeRecycle: Reclaiming Guarantees from Probabilistic Certificates for Stochastic Dynamical Systems after Change

TL;DR

VeRecycle is a novel framework that efficiently reuses probabilistic certificates to verify safety in stochastic dynamical systems after localized changes, reducing re-certification costs.

Contribution

It introduces the first method to reclaim guarantees from probabilistic certificates for stochastic systems with localized dynamics changes, enhancing efficiency and scalability.

Findings

VeRecycle reduces re-certification computational costs.

It maintains competitive probabilistic safety guarantees.

The framework is applicable to neural control in stochastic systems.

Abstract

Autonomous systems operating in the real world encounter a range of uncertainties. Probabilistic neural Lyapunov certification is a powerful approach to proving safety of nonlinear stochastic dynamical systems. When faced with changes beyond the modeled uncertainties, e.g., unidentified obstacles, probabilistic certificates must be transferred to the new system dynamics. However, even when the changes are localized in a known part of the state space, state-of-the-art requires complete re-certification, which is particularly costly for neural certificates. We introduce VeRecycle, the first framework to formally reclaim guarantees for discrete-time stochastic dynamical systems. VeRecycle efficiently reuses probabilistic certificates when the system dynamics deviate only in a given subset of states. We present a general theoretical justification and algorithmic implementation. Our experimental evaluation shows scenarios where VeRecycle both saves significant computational effort and achieves competitive probabilistic guarantees in compositional neural control.