SCAFFLSA: Taming Heterogeneity in Federated Linear Stochastic Approximation and TD Learning
This addresses communication bottlenecks in federated learning for heterogeneous agents, offering incremental improvements over existing methods like Scaffnew.
The paper tackles the problem of high communication complexity in federated linear stochastic approximation due to agent heterogeneity, and proposes SCAFFLSA, a variant that reduces communication complexity to logarithmic scaling with accuracy while achieving linear speed-up in sample complexity with the number of agents.
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.