Byzantine-Resilient Decentralized TD Learning with Linear Function Approximation

This paper considers the policy evaluation problem in reinforcement learning with agents of a decentralized and directed network. 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(λ) collaboratively. However, when some Byzantine agents behave adversarially, decentralized TD(λ) is unable to learn an accurate linear approximation for the true value function. We propose a trimmed-mean based decentralized TD(λ) algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error that depends on the number of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm.