Distributionally Robust Federated Averaging

TL;DR

This paper introduces a novel communication-efficient federated learning algorithm, DRFA, designed for distributionally robust optimization, with proven convergence and experimental validation.

Contribution

It proposes the DRFA algorithm with a snapshotting scheme for distributionally robust federated learning, analyzing its convergence in various settings and extending to regularized objectives.

Findings

DRFA achieves convergence in convex and nonconvex settings.

The proximal variant DRFA-Prox converges with provable rates.

Experimental results support theoretical claims.

Abstract

In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax structure of the underlying optimization problem, a key difficulty arises from the fact that the global parameter that controls the mixture of local losses can only be updated infrequently on the global stage. To compensate for this, we propose a Distributionally Robust Federated Averaging (DRFA) algorithm that employs a novel snapshotting scheme to approximate the accumulation of history gradients of the mixing parameter. We analyze the convergence rate of DRFA in both convex-linear and nonconvex-linear settings. We also generalize the proposed idea to objectives with regularization on the mixture parameter and propose a proximal variant, dubbed as DRFA-Prox, with provable convergence rates. We also analyze an alternative optimization method for regularized cases in strongly-convex-strongly-concave and non-convex (under PL condition)-strongly-concave settings. To the best of our knowledge, this paper is the first to solve distributionally robust federated learning with reduced communication, and to analyze the efficiency of local descent methods on distributed minimax problems. We give corroborating experimental evidence for our theoretical results in federated learning settings.