Importance Sampling for Statistical Certification of Viable Initial Sets

TL;DR

This paper introduces a simulation-based importance sampling framework with finite-sample guarantees to efficiently certify viable initial sets in complex models.

Contribution

It develops a novel importance sampling method with empirical Bernstein bounds for finite-sample statistical certification of viability in black-box models.

Findings

Effective certification of VISs in two systems.

Improved convergence of bounds on an Adaptive Cruise Control benchmark.

Abstract

We study the problem of statistically certifying viable initial sets (VISs) -- sets of initial conditions whose trajectories satisfy a given control specification. While VISs can be obtained from model-based methods, these methods typically rely on simplified models. We propose a simulation-based framework to certify VISs by estimating the probability of specification violations under a high-fidelity or black-box model. Since detecting these violations may be challenging due to their scarcity, we propose a sample-efficient framework that leverages importance sampling to target high-risk regions. We derive an empirical Bernstein inequality for weighted random variables, enabling finite-sample guarantees for importance sampling estimators. We demonstrate the effectiveness of the proposed approach on two systems and show improved convergence of the resulting bounds on an Adaptive Cruise Control benchmark.