A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems

• URL: http://arxiv.org/abs/2106.06075v1
• Date: Thu, 10 Jun 2021 22:32:01 GMT
• Title: A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems
• Authors: Babak Barazandeh, Tianjian Huang, George Michailidis
• Abstract summary: We develop a decentralized adaptive momentum (ADAM)-type algorithm for solving min-max optimization problem. We obtain non-asymptotic rates of convergence of the proposed algorithm for finding a (stochastic) first-order Nash equilibrium point.
• Score: 9.653157073271021
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 efforts 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.

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