Byzantine-Resilient Decentralized TD Learning with Linear Function Approximation

TL;DR

This paper introduces a Byzantine-resilient decentralized TD learning algorithm with linear function approximation, capable of accurately evaluating policies in multi-agent reinforcement learning environments despite malicious agents.

Contribution

It proposes a novel trimmed-mean based algorithm that ensures robustness and convergence in the presence of Byzantine agents in decentralized RL.

Findings

The algorithm converges at a finite-time rate.

It maintains accurate policy evaluation despite Byzantine adversaries.

Numerical experiments confirm robustness and effectiveness.

Abstract

This paper considers the policy evaluation problem in a multi-agent reinforcement learning (MARL) environment over decentralized and directed networks. The focus is on decentralized temporal difference (TD) learning with linear function approximation in the presence of unreliable or even malicious agents, termed as Byzantine agents. In order to evaluate the quality of a fixed policy in a common environment, agents usually run decentralized TD($\lambda$) collaboratively. However, when some Byzantine agents behave adversarially, decentralized TD($\lambda$) is unable to learn an accurate linear approximation for the true value function. We propose a trimmed-mean based Byzantine-resilient decentralized TD($\lambda$) algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error in the presence of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm.