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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

Indonesian

Set-set reach-avoid, yang mendefinisikan keadaan dari mana suatu tugas dapat diselesaikan sambil menghindari wilayah yang tidak aman, adalah alat dasar untuk mengimplementasikan robot di lingkungan yang terkena gangguan dan ketidakpastian, serta untuk pemantauan kelayakan tugas runtime, memungkinkan prediksi apakah suatu keadaan aman dan akan mengarah ke penyelesaian tugas yang sukses. Classic Hamilton-Jacobi Reachability (HJR) dan ekstensi saraf baru-baru ini (misalnya, Lipschitz Continuous Task Reachability Learning, DeepReach) memperlakukan gangguan secara adversarial, menghitung set reach-avoid di bawah gangguan terburuk dari set terbatas. Ini menjamin keamanan tetapi dapat menghasilkan set-set yang terlalu konservatif ketika gangguan adalah stochastic daripada adversarial, dan juga potensial memerlukan gangguan yang ditetapkan untuk diketahui atau ditentukan sebelumnya

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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