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

2025-05-20

AI Summary

Existing probabilistic neural Lyapunov certificates fail under dynamic abrupt changes (e.g., unknown obstacles), necessitating costly full-system re-certification. Method: We propose the first reusable probabilistic neural Lyapunov certification framework for discrete-time stochastic dynamical systems. Its core insight is that when dynamics deviate only over a known subset of the state space, certification need not be recomputed globally; instead, only the locally perturbed region requires certificate update. Our approach integrates probabilistic neural Lyapunov function modeling, localized deviation detection, and a novel certificate composition and reuse algorithm enabling incremental safety guarantee recovery. Contribution/Results: We theoretically prove that the reused certificate preserves the original probabilistic safety guarantee under local perturbations. Experiments demonstrate substantial computational savings—up to an order of magnitude—while maintaining safety guarantees statistically equivalent to full re-certification across composite neural control tasks.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production 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.

Problem

• Reclaiming safety guarantees for stochastic systems after dynamic changes
• Efficient reuse of probabilistic certificates for localized state changes
• Reducing computational cost of re-certification in neural control systems

Innovation

• Reuses probabilistic certificates for changed dynamics
• Localizes changes to avoid complete re-certification
• Efficiently maintains guarantees in stochastic systems