Federated Distributional Reinforcement Learning with Distributional Critic Regularization

Federated reinforcement learning typically aggregates value functions or policies by parameter averaging, which emphasizes expected return and can obscure statistical multimodality and tail behavior that matter in safety-critical settings. We formalize federated distributional reinforcement learning (FedDistRL), where clients parametrize quantile value function critics and federate these networks only. We also propose TR-FedDistRL, which builds a per client, risk-aware Wasserstein barycenter over a temporal buffer. This local barycenter provides a reference region to constrain the parameter averaged critic, ensuring necessary distributional information is not averaged out during the federation process. The distributional trust region is implemented as a shrink-squash step around this reference. Under fixed-policy evaluation, the feasibility map is nonexpansive and the update is contractive in a probe-set Wasserstein metric under evaluation. Experiments on a bandit, multi-agent gridworld, and continuous highway environment show reduced mean-smearing, improved safety proxies (catastrophe/accident rate), and lower critic/policy drift versus mean-oriented and non-federated baselines.