Publication Type

Journal Article

Version

publishedVersion

Publication Date

8-2022

Abstract

Emerging applications in multiagent environments such as internet-of-things, networked sensing, autonomous systems, and federated learning, call for decentralized algorithms for finite-sum optimizations that are resource efficient in terms of both computation and communication. In this paper, we consider the prototypical setting where the agents work collaboratively to minimize the sum of local loss functions by only communicating with their neighbors over a predetermined network topology. We develop a new algorithm, called DEcentralized STochastic REcurSive gradient methodS (DESTRESS) for nonconvex finite-sum optimization, which matches the optimal incremental first-order oracle complexity of centralized algorithms for finding first-order stationary points, while maintaining communication efficiency. Detailed theoretical and numerical comparisons corroborate that the resource efficiencies of DESTRESS improve upon prior decentralized algorithms over a wide range of parameter regimes. DESTRESS leverages several key algorithm design ideas including stochastic recursive gradient updates with minibatches for local computation, gradient tracking with extra mixing (i.e., multiple gossiping rounds) for periteration communication, together with careful choices of hyperparameters and new analysis frameworks to provably achieve a desirable computation-communication trade-off.

Keywords

decentralized optimization, nonconvex finite-sum optimization, stochastic recursive gradient methods

Discipline

Databases and Information Systems

Research Areas

Data Science and Engineering; Intelligent Systems and Optimization

Publication

SIAM Journal on Mathematics of Data Science

Volume

4

Issue

3

First Page

1031

Last Page

1051

Identifier

10.1137/21M1450677

Publisher

Society for Industrial and Applied Mathematics

Additional URL

https://doi.org/10.1137/21M1450677

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