Zhijie Xie

Zhijie Xie, S. H. Song

As a distributed learning paradigm, Federated Learning (FL) faces the communication bottleneck issue due to many rounds of model synchronization and aggregation. Heterogeneous data further deteriorates the situation by causing slow convergence. Although the impact of data heterogeneity on supervised FL has been widely studied, the related investigation for Federated Reinforcement Learning (FRL) is still in its infancy. In this paper, we first define the type and level of data heterogeneity for policy gradient based FRL systems. By inspecting the connection between the global and local objective functions, we prove that local training can benefit the global objective, if the local update is properly penalized by the total variation (TV) distance between the local and global policies. A necessary condition for the global policy to be learn-able from the local policy is also derived, which is directly related to the heterogeneity level. Based on the theoretical result, a Kullback-Leibler (KL) divergence based penalty is proposed, which, different from the conventional method that penalizes the model divergence in the parameter space, directly constrains the model outputs in the distribution space. Convergence proof of the proposed algorithm is also provided. By jointly penalizing the divergence of the local policy from the global policy with a global penalty and constraining each iteration of the local training with a local penalty, the proposed method achieves a better trade-off between training speed (step size) and convergence. Experiment results on two popular Reinforcement Learning (RL) experiment platforms demonstrate the advantage of the proposed algorithm over existing methods in accelerating and stabilizing the training process with heterogeneous data.

Zhijie Xie, Shenghui Song

In the context of Federated Reinforcement Learning (FRL), applying Proximal Policy Optimization (PPO) faces challenges related to the update order of its actor and critic due to the aggregation step occurring between successive iterations. In particular, when local actors are updated based on local critic estimations, the algorithm becomes vulnerable to data heterogeneity. As a result, the conventional update order in PPO (critic first, then actor) may cause heterogeneous gradient directions among clients, hindering convergence to a globally optimal policy. To address this issue, we propose FedRAC, which reverses the update order (actor first, then critic) to eliminate the divergence of critics from different clients. Theoretical analysis shows that the convergence bound of FedRAC is immune to data heterogeneity under mild conditions, i.e., bounded level of heterogeneity and accurate policy evaluation. Empirical results indicate that the proposed algorithm obtains higher cumulative rewards and converges more rapidly in five experiments, including three classical RL environments and a highly heterogeneous autonomous driving scenario using the SUMO traffic simulator.

Zhijie Xie, Shenghui Song

The development of Policy Iteration (PI) has inspired many recent algorithms for Reinforcement Learning (RL), including several policy gradient methods that gained both theoretical soundness and empirical success on a variety of tasks. The theory of PI is rich in the context of centralized learning, but its study under the federated setting is still in the infant stage. This paper investigates the federated version of Approximate PI (API) and derives its error bound, taking into account the approximation error introduced by environment heterogeneity. We theoretically prove that a proper client selection scheme can reduce this error bound. Based on the theoretical result, we propose a client selection algorithm to alleviate the additional approximation error caused by environment heterogeneity. Experiment results show that the proposed algorithm outperforms other biased and unbiased client selection methods on the federated mountain car problem, the Mujoco Hopper problem, and the SUMO-based autonomous vehicle training problem by effectively selecting clients with a lower level of heterogeneity from the population distribution.