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

TL;DR

This paper introduces a deep reinforcement learning approach to compute reach-avoid sets in infinite-horizon zero-sum games, enabling control under worst-case disturbances with theoretical guarantees.

Contribution

It develops a new value function with a contracting Bellman backup and extends Conservative Q-Learning to high-dimensional reach-avoid problems.

Findings

The method reliably learns reach-avoid sets with neural networks.

The approach can compute viability kernels and backward reachable sets.

Empirical results demonstrate effectiveness in complex scenarios.

Abstract

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.