Federated Temporal Difference Learning with Linear Function Approximation under Environmental Heterogeneity

TL;DR

This paper provides the first finite-time analysis of federated TD learning with linear function approximation, demonstrating linear speedups in policy evaluation under low environmental heterogeneity.

Contribution

It introduces a comprehensive analysis of federated TD learning considering heterogeneity, Markovian sampling, and communication efficiency, with novel perturbation bounds and a virtual MDP framework.

Findings

Exchanging information accelerates policy evaluation in low-heterogeneity settings.

The analysis establishes conditions for linear convergence speedups with multiple agents.

Novel perturbation bounds relate heterogeneity to TD fixed points.

Abstract

We initiate the study of federated reinforcement learning under environmental heterogeneity by considering a policy evaluation problem. Our setup involves $N$ agents interacting with environments that share the same state and action space but differ in their reward functions and state transition kernels. Assuming agents can communicate via a central server, we ask: Does exchanging information expedite the process of evaluating a common policy? To answer this question, we provide the first comprehensive finite-time analysis of a federated temporal difference (TD) learning algorithm with linear function approximation, while accounting for Markovian sampling, heterogeneity in the agents' environments, and multiple local updates to save communication. Our analysis crucially relies on several novel ingredients: (i) deriving perturbation bounds on TD fixed points as a function of the heterogeneity in the agents' underlying Markov decision processes (MDPs); (ii) introducing a virtual MDP to closely approximate the dynamics of the federated TD algorithm; and (iii) using the virtual MDP to make explicit connections to federated optimization. Putting these pieces together, we rigorously prove that in a low-heterogeneity regime, exchanging model estimates leads to linear convergence speedups in the number of agents.