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Stochastic Minimum-Cost Reach-Avoid Reinforcement Learning

arXiv 2605.11975 ↗First posted 12 May 2026cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 52 references that are in the map. First posted on arXiv 12 May 2026.

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References · 31

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19 more
  1. 2020Projection-Based Constrained Policy Optimizationcited by 195
  2. 2015Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approachcited by 162
  3. 2018Crowd-Robot Interaction: Crowd-aware Robot Navigation with Attention-based Deep Reinforcement Learningcited by 162
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  10. 2023Solving Stabilize-Avoid Optimal Control via Epigraph Form and Deep Reinforcement Learningcited by 24
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  12. 2024Balance Reward and Safety Optimization for Safe Reinforcement Learning: A Perspective of Gradient Manipulationcited by 21
  13. 2024Solving Minimum-Cost Reach Avoid using Reinforcement Learningcited by 14
  14. 2024Reinforcement Learning with LTL and ω-Regular Objectives via Optimality-Preserving Translation to Average Rewardscited by 13
  15. 2023Compositional Policy Learning in Stochastic Control Systems with Formal Guaranteescited by 12
  16. 2024Q-learning for Quantile MDPs: A Decomposition, Performance, and Convergence Analysiscited by 6
  17. 2024Sufficient and Necessary Barrier-like Conditions for Safety and Reach-avoid Verification of Stochastic Discrete-time Systemscited by 2
  18. 2023An alternating peak-optimization method for optimal trajectory generation of quadrotor dronescited by 1
  19. 2025Comparative Analysis of Barrier-like Function Methods for Reach-Avoid Verification in Stochastic Discrete-Time Systemscited by 1

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