Federated Temporal Difference Learning with Linear Function Approximation under Environmental Heterogeneity
This addresses the challenge of efficient policy evaluation in federated settings with heterogeneous environments, which is incremental as it extends existing federated learning to reinforcement learning with new theoretical guarantees.
The paper tackles the problem of federated reinforcement learning under environmental heterogeneity by analyzing a federated temporal difference learning algorithm for policy evaluation, proving that exchanging model estimates leads to linear convergence speedups in the number of agents in low-heterogeneity regimes.
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.