Federated Accelerated Stochastic Gradient Descent

TL;DR

This paper introduces FedAc, an accelerated federated learning algorithm that improves convergence speed and reduces communication rounds compared to FedAvg, especially for convex functions, through novel stability and potential-based analysis.

Contribution

FedAc is the first provably accelerated version of FedAvg, achieving faster convergence and fewer communication rounds for convex optimization in federated learning.

Findings

FedAc achieves linear speedup with fewer rounds of communication.

FedAc outperforms FedAvg in convergence speed on convex functions.

Stronger guarantees for third-order smooth objectives.

Abstract

We propose Federated Accelerated Stochastic Gradient Descent (FedAc), a principled acceleration of Federated Averaging (FedAvg, also known as Local SGD) for distributed optimization. FedAc is the first provable acceleration of FedAvg that improves convergence speed and communication efficiency on various types of convex functions. For example, for strongly convex and smooth functions, when using $M$ workers, the previous state-of-the-art FedAvg analysis can achieve a linear speedup in $M$ if given $M$ rounds of synchronization, whereas FedAc only requires $M^{\frac{1}{3}}$ rounds. Moreover, we prove stronger guarantees for FedAc when the objectives are third-order smooth. Our technique is based on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability.