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Temporal Difference Learning of Probabilistic Reach-Avoid Value Functions

Elias Fontanari, Pietro Noah Crestaz, Matteo Saveriano, Andrea Del Prete · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28106 · cited by 0 works (OpenAlex) · open-access PDF

Japanese

危険な地域を避ける一方で任務を完了できる状態を定義するリードセットは、障害や不確実性に直面する環境でロボットを展開するための基本的なツールであり、ランタイムタスク実行可能性のモニタリングのために、状態が安全であるかどうかを予測することを可能にします。クラシックハミルトン・ジャコビー・レイチャビリティ(HJR)とその最近のニューラル拡張(例えば、リップシッツ・Continuous Task Reachability Learning、DeepReach)は、障害を対立的に扱い、最悪の障害の下でリードされたリードセットを計算することを可能にします。これはセキュリティを保証しますが、障害がストカス主義ではなく対立主義であるときには過度に保守

Machine translation (Meta M2M100); the English original follows.

Abstract

Reach-avoid sets, defining the states from which a task can be completed while avoiding unsafe regions, are fundamental tools for deploying robots in environments subject to disturbances and uncertainty, as well as for runtime task-feasibility monitoring, allowing prediction of whether a state is safe and will lead to successful task completion. Classical Hamilton-Jacobi Reachability (HJR) and its recent neural extensions (e.g., Lipschitz Continuous Reachability Learning, DeepReach) treat disturbances adversarially, computing the reach-avoid set under worst-case disturbances from a bounded set. This guarantees safety but can yield overly conservative sets when disturbances are stochastic rather than adversarial, and additionally requires the disturbance set to be known or specified in advance. We propose Probabilistic reach-avoid Value Function (PVF), a self-supervised method, applicable to black-box systems, for computing reach-avoid sets as the states with a certain reach-avoid probability under stochastic, potentially unbounded disturbances. We evaluate our approach against HJR-based baselines on systems of increasing complexity, up to a Hopper locomotion task, and show that our probabilistic sets are less conservative and more accurate than adversarial HJR sets when disturbances are non-adversarial.

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Topics: Probabilistic logic, Reachability, Set (abstract data type), Bounded function, Task (project management), Computer science

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