Yiling Xue

Taoran Wu, Yiling Xue, Jingduo Pan et al.

Identifying controlled safety invariant sets (CSISs) is essential for safety-critical systems. This paper addresses the problem of computing CSISs for black-box discrete-time systems, where the dynamics are unknown and only limited simulation data are available. Traditionally, a CSIS requires that for every state in the set, there exists a control input that keeps the system within the set at the next step. However, enforcing such universal invariance, i.e., requiring the set to remain controlled invariant for all states, is often overly restrictive or impractical for black-box systems. To address this, we introduce the notion of a Probably Approximately Correct (PAC) CSIS, in which, with prescribed confidence, there exists a suitable control input to keep the system within the set at the next step for at least a specified fraction of the states. Our approach leverages barrier functions and scenario optimization, yielding a tractable linear programming method for estimating PAC CSISs. Several illustrative examples demonstrate the effectiveness of the proposed framework.

Jingduo Pan, Taoran Wu, Yiling Xue et al.

We study stochastic minimum-cost reach-avoid reinforcement learning, where an agent must satisfy a reach-avoid specification with probability at least $p$ while minimizing expected cumulative costs in stochastic environments. Existing safe and constrained reinforcement learning methods typically fail to jointly enforce probabilistic reach-avoid constraints and optimize cost in the learning setting in stochastic environments. To address this challenge, we introduce reach-avoid probability certificates (RAPCs), which identify states from which stochastic reach-avoid constraints are satisfiable. Building on RAPCs, we develop a contraction-based Bellman formulation that serves as a principled surrogate for integrating reach-avoid considerations into reinforcement learning, enabling cost optimization under probabilistic constraints. We establish almost sure convergence of the proposed algorithms to locally optimal policies with respect to the resulting objective. Experiments in the MuJoCo simulator demonstrate improved cost performance and consistently higher reach-avoid satisfaction rates.