SCAFFLSA: Taming Heterogeneity in Federated Linear Stochastic Approximation and TD Learning

Paul Mangold, Sergey Samsonov, Safwan Labbi, Ilya Levin, Reda ALAMI, Alexey Naumov, Eric Moulines

Keywords: Stochastic Approximation, Reinforcement learning, Federated Learning, Machine Learning

TL;DR: We perform a non-asymptotic analysis of federated LSA, study the impcaft of heterogeneity, and propose a method that mitigates this impact by using control variates while preserving the linear speed-up. We apply the results to federated TD.

Abstract: In this paper, we analyze the sample and communication complexity of the federated linear stochastic approximation (FedLSA) algorithm. We explicitly quantify the effects of local training with agent heterogeneity. We show that the communication complexity of FedLSA scales polynomially with the inverse of the desired accuracy ϵ. To overcome this, we propose SCAFFLSA a new variant of FedLSA that uses control variates to correct for client drift, and establish its sample and communication complexities. We show that for statistically heterogeneous agents, its communication complexity scales logarithmically with the desired accuracy, similar to Scaffnew. An important finding is that, compared to the existing results for Scaffnew, the sample complexity scales with the inverse of the number of agents, a property referred to as linear speed-up. Achieving this linear speed-up requires completely new theoretical arguments. We apply the proposed method to federated temporal difference learning with linear function approximation and analyze the corresponding complexity improvements.

Primary Area: Reinforcement learning

Submission Number: 7376