Near-Optimal Decentralized Momentum Method for Nonconvex-PL Minimax Problems

TL;DR

This paper introduces a decentralized momentum-based gradient method for nonconvex-PL stochastic minimax problems, achieving near-optimal convergence rates in distributed machine learning scenarios.

Contribution

It proposes the first decentralized algorithm for nonconvex-PL stochastic minimax problems with theoretical convergence guarantees.

Findings

Achieves near-optimal gradient complexity of O(ε^{-3})

First to study decentralized algorithms for nonconvex-PL minimax problems

Convergence analysis confirms efficiency in distributed settings

Abstract

Minimax optimization plays an important role in many machine learning tasks such as generative adversarial networks (GANs) and adversarial training. Although recently a wide variety of optimization methods have been proposed to solve the minimax problems, most of them ignore the distributed setting where the data is distributed on multiple workers. Meanwhile, the existing decentralized minimax optimization methods rely on the strictly assumptions such as (strongly) concavity and variational inequality conditions. In the paper, thus, we propose an efficient decentralized momentum-based gradient descent ascent (DM-GDA) method for the distributed nonconvex-PL minimax optimization, which is nonconvex in primal variable and is nonconcave in dual variable and satisfies the Polyak-Lojasiewicz (PL) condition. In particular, our DM-GDA method simultaneously uses the momentum-based techniques to update variables and estimate the stochastic gradients. Moreover, we provide a solid convergence analysis for our DM-GDA method, and prove that it obtains a near-optimal gradient complexity of $O(\epsilon^{-3})$ for finding an $\epsilon$-stationary solution of the nonconvex-PL stochastic minimax problems, which reaches the lower bound of nonconvex stochastic optimization. To the best of our knowledge, we first study the decentralized algorithm for Nonconvex-PL stochastic minimax optimization over a network.