A Stochastic Second-Order Proximal Method for Distributed Optimization

TL;DR

This paper introduces St-SoPro, a distributed stochastic second-order proximal method that efficiently minimizes local loss functions across a network, achieving faster convergence and lower costs compared to existing methods.

Contribution

The paper presents a novel decentralized second-order approximation algorithm, St-SoPro, that improves distributed optimization by combining stochastic sampling with second-order information.

Findings

St-SoPro achieves linear convergence rate for strongly convex problems.

The method outperforms state-of-the-art first-order algorithms in speed and efficiency.

Simulations on real datasets confirm superior convergence and cost performance.

Abstract

In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm, referred to as St-SoPro, incorporates a decentralized second-order approximation into an augmented Lagrangian function, and then randomly samples the local gradients and Hessian matrices of the agents, so that it is computationally and memory-wise efficient, particularly for large-scale optimization problems. We show that for globally restricted strongly convex problems, the expected optimality error of St-SoPro asymptotically drops below an explicit error bound at a linear rate, and the error bound can be arbitrarily small with proper parameter settings. Simulations over real machine learning datasets demonstrate that St-SoPro outperforms several state-of-the-art distributed stochastic first-order methods in terms of convergence speed as well as computation and communication costs.