Sample-based and Feature-based Federated Learning for Unconstrained and Constrained Nonconvex Optimization via Mini-batch SSCA

TL;DR

This paper introduces novel federated learning algorithms based on stochastic successive convex approximation (SSCA) for both unconstrained and constrained nonconvex problems, demonstrating improved convergence and efficiency over traditional methods.

Contribution

It develops and analyzes FL algorithms using SSCA and mini-batch techniques for unconstrained and constrained nonconvex optimization, establishing convergence to stationary and KKT points.

Findings

Algorithms converge to stationary and KKT points.

Proposed methods outperform traditional SGD in convergence speed.

Algorithms have appealing computational and communication complexity.

Abstract

Federated learning (FL) has become a hot research area in enabling the collaborative training of machine learning models among multiple clients that hold sensitive local data. Nevertheless, unconstrained federated optimization has been studied mainly using stochastic gradient descent (SGD), which may converge slowly, and constrained federated optimization, which is more challenging, has not been investigated so far. This paper investigates sample-based and feature-based federated optimization, respectively, and considers both unconstrained and constrained nonconvex problems for each of them. First, we propose FL algorithms using stochastic successive convex approximation (SSCA) and mini-batch techniques. These algorithms can adequately exploit the structures of the objective and constraint functions and incrementally utilize samples. We show that the proposed FL algorithms converge to stationary points and Karush-Kuhn-Tucker (KKT) points of the respective unconstrained and constrained nonconvex problems, respectively. Next, we provide algorithm examples with appealing computational complexity and communication load per communication round. We show that the proposed algorithm examples for unconstrained federated optimization are identical to FL algorithms via momentum SGD and provide an analytical connection between SSCA and momentum SGD. Finally, numerical experiments demonstrate the inherent advantages of the proposed algorithms in convergence speeds, communication and computation costs, and model specifications.