Paper Info
Title
A Decentralized Adaptive Momentum Method For Solving A Class Of Min-Max Optimization Problems
Abstract
Min-max saddle point games have recently been intensely studied, due to their wide range of applications, including training Generative Adversarial Networks (GANs). However, most of the recent effort s for solving them are limited to special regimes such as convex-concave games. Further, it is customarily assumed that the underlying optimization problem is solved either by a single machine or in the case of multiple machines connected in centralized fashion, wherein each one communicates with a central node. The latter approach becomes challenging, when the underlying communications network has low bandwidth. In addition, privacy considerations may dictate that certain nodes can communicate with a subset of other nodes. Hence, it is of interest to develop methods that solve min-max games in a decentralized manner. To that end, we develop a decentralized adaptive momentum (ADAM)-type algorithm for solving min-max optimization problem under the condition that the objective function satisfies a Minty Variational Inequality condition, which is a generalization to convex-concave case. The proposed method overcomes shortcomings of recent non-adaptive gradient-based decentralized algorithms for min max optimization problems, that do not perform well in practice and require careful tuning. In this paper, we obtain non-asymptotic rates of convergence of the proposed algorithm (coined DADAM(3) ) for finding a (stochastic) first-order Nash equilibrium point and subsequently evaluate its performance on training GANs. The extensive empirical evaluation shows that DADAM(3) outperforms recently developed methods, including decentralized optimistic stochastic gradient for solving such min-max problems. (c) 2021 Elsevier B.V. All rights reserved.
Year
DOI
Venue
2021
10.1016/j.sigpro.2021.108245
SIGNAL PROCESSING
Keywords
DocType
Volume
First-order nash equilibria, Stationary points, Distributed optimization, Non-convex min-max problems, Variational inequality, First-order Nash equilibria
Journal
189
ISSN
Citations 
PageRank 
0165-1684
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Babak Barazandeh100.68
Huang Tianjian221.04
George Michailidis304.73