Zero-Sum Positional Differential Games as a Framework for Robust Reinforcement Learning: Deep Q-Learning Approach

TL;DR

This paper introduces a novel framework for Robust Reinforcement Learning using zero-sum positional differential games, providing a theoretical basis and a deep Q-learning approach that outperforms existing methods in various environments.

Contribution

It is the first to apply positional differential game theory to RRL, deriving a centralized Q-learning method with theoretical guarantees under Isaacs's condition.

Findings

The proposed Isaacs Deep Q-Network outperforms baseline algorithms.

Theoretical justification for using a single Q-function for minimax and maximin problems.

Demonstrated effectiveness in diverse environments.

Abstract

Robust Reinforcement Learning (RRL) is a promising Reinforcement Learning (RL) paradigm aimed at training robust to uncertainty or disturbances models, making them more efficient for real-world applications. Following this paradigm, uncertainty or disturbances are interpreted as actions of a second adversarial agent, and thus, the problem is reduced to seeking the agents' policies robust to any opponent's actions. This paper is the first to propose considering the RRL problems within the positional differential game theory, which helps us to obtain theoretically justified intuition to develop a centralized Q-learning approach. Namely, we prove that under Isaacs's condition (sufficiently general for real-world dynamical systems), the same Q-function can be utilized as an approximate solution of both minimax and maximin Bellman equations. Based on these results, we present the Isaacs Deep Q-Network algorithms and demonstrate their superiority compared to other baseline RRL and Multi-Agent RL algorithms in various environments.