Second-Order Guarantees in Federated Learning

TL;DR

This paper establishes second-order guarantees for federated learning algorithms, addressing the challenge of saddle points in non-convex deep learning models under federated settings.

Contribution

It extends theoretical analysis to second-order optimality in federated learning, a novel contribution beyond existing first-order analyses.

Findings

Provides second-order guarantees for federated learning algorithms.

Addresses saddle-point issues in non-convex federated optimization.

Bridges centralized and decentralized stochastic gradient results.

Abstract

Federated learning is a useful framework for centralized learning from distributed data under practical considerations of heterogeneity, asynchrony, and privacy. Federated architectures are frequently deployed in deep learning settings, which generally give rise to non-convex optimization problems. Nevertheless, most existing analysis are either limited to convex loss functions, or only establish first-order stationarity, despite the fact that saddle-points, which are first-order stationary, are known to pose bottlenecks in deep learning. We draw on recent results on the second-order optimality of stochastic gradient algorithms in centralized and decentralized settings, and establish second-order guarantees for a class of federated learning algorithms.