mlsanityData to 7 Oct 2026

Infinite-Horizon Reach-Avoid Zero-Sum Games via Deep Reinforcement Learning

arXiv 2203.10142 ↗First posted 18 Mar 2022eess.SY cs.AI cs.LGcited by 6

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Abstract (arXiv)

In this paper, we consider the infinite-horizon reach-avoid zero-sum game problem, where the goal is to find a set in the state space, referred to as the reach-avoid set, such that the system starting at a state therein could be controlled to reach a given target set without violating constraints under the worst-case disturbance. We address this problem by designing a new value function with a contracting Bellman backup, where the super-zero level set, i.e., the set of states where the value function is evaluated to be non-negative, recovers the reach-avoid set. Building upon this, we prove that the proposed method can be adapted to compute the viability kernel, or the set of states which could be controlled to satisfy given constraints, and the backward reachable set, or the set of states that could be driven towards a given target set. Finally, we propose to alleviate the curse of dimensionality issue in high-dimensional problems by extending Conservative Q-Learning, a deep reinforcement learning technique, to learn a value function such that the super-zero level set of the learned value function serves as a (conservative) approximation to the reach-avoid set. Our theoretical and empirical results suggest that the proposed method could learn reliably the reach-avoid set and the optimal control policy even with neural network approximation.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 17 of its 35 references that are in the map. First posted on arXiv 18 Mar 2022.

Builds on

17 of 35 references.

References · 17

  1. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,635
  2. 2013Playing Atari with Deep Reinforcement Learningcited by 3,211
  3. 2020Conservative Q-Learning for Offline Reinforcement Learningcited by 1,777
  4. 2017Constrained Policy Optimizationcited by 928
  5. 2015Risk-Constrained Reinforcement Learning with Percentile Risk Criteriacited by 320
  6. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
  7. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 261
  8. 2019A Theoretical Analysis of Deep Q-Learningcited by 212
  9. 2017Hamilton-Jacobi Reachability: A Brief Overview and Recent Advancescited by 186
  10. 2020DeepReach: A Deep Learning Approach to High-Dimensional Reachabilitycited by 81
  11. 2021Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learningcited by 43
  12. 2014Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraintscited by 41
5 more
  1. 2016Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systemscited by 16
  2. 2018Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approachcited by 8
  3. 2018Reach-Avoid Problems via Sum-of-Squares Optimization and Dynamic Programmingcited by 4
  4. 2017Underapproximation of Reach-Avoid Sets for Discrete-Time Stochastic Systems via Lagrangian Methodscited by 3
  5. 2016Exact and Efficient Hamilton-Jacobi-based Guaranteed Safety Analysis via System Decompositioncited by 2

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Cited by year

Citing papers per year: 2023: 1; 2024: 5.

6 papers.

  1. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 77
  2. 2024Safe Multi-Agent Reinforcement Learning with Convergence to Generalized Nash Equilibriumcited by 5
  3. 2024Do No Harm: A Counterfactual Approach to Safe Reinforcement Learningcited by 1
  4. 2024Zero-Sum Positional Differential Games as a Framework for Robust Reinforcement Learning: Deep Q-Learning Approachcited by 0
  5. 2024A Safe Exploration Strategy for Model-free Task Adaptation in Safety-constrained Grid Environmentscited by 0
  6. 2024Deep Reinforcement Learning for Reach-Avoid-Stay Problemscited by 0