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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

German

Reach-Avoid-Sets, die die Zustände definieren, aus denen eine Aufgabe abgeschlossen werden kann, während unsichere Regionen vermieden werden, sind grundlegende Werkzeuge für die Bereitstellung von Robotern in Umgebungen, die von Störungen und Unsicherheiten betroffen sind, sowie für die Laufzeit-Task-Avoid-Überwachung, die Vorhersage ermöglicht, ob ein Zustand sicher ist und zu einem erfolgreichen Abschluss führen wird. Klassische Hamilton-Jacobi Reachability (HJR) und seine jüngsten neuronalen Erweiterungen (z. B. Lipschitz Continuous Task Reachability Learning, DeepReach) behandeln Störungen adversarisch und berechnen den Reach-Avoid-Set unter den schlimmsten Störungen aus einer begren

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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