Towards Fast Rates for Federated and Multi-Task Reinforcement Learning
This addresses the challenge of efficient collaboration in multi-agent RL for applications like robotics or autonomous systems, though it appears incremental by building on existing policy gradient methods.
The paper tackles the problem of federated and multi-task reinforcement learning with heterogeneous agents, proposing Fast-FedPG to achieve globally optimal policies without bias, with results including fast linear convergence and sub-linear rates with linear speedup.
We consider a setting involving $N$ agents, where each agent interacts with an environment modeled as a Markov Decision Process (MDP). The agents' MDPs differ in their reward functions, capturing heterogeneous objectives/tasks. The collective goal of the agents is to communicate intermittently via a central server to find a policy that maximizes the average of long-term cumulative rewards across environments. The limited existing work on this topic either only provide asymptotic rates, or generate biased policies, or fail to establish any benefits of collaboration. In response, we propose Fast-FedPG - a novel federated policy gradient algorithm with a carefully designed bias-correction mechanism. Under a gradient-domination condition, we prove that our algorithm guarantees (i) fast linear convergence with exact gradients, and (ii) sub-linear rates that enjoy a linear speedup w.r.t. the number of agents with noisy, truncated policy gradients. Notably, in each case, the convergence is to a globally optimal policy with no heterogeneity-induced bias. In the absence of gradient-domination, we establish convergence to a first-order stationary point at a rate that continues to benefit from collaboration.