Solving a class of non-convex min-max games using adaptive momentum methods

TL;DR

This paper introduces an adaptive momentum min-max algorithm tailored for non-convex min-max problems, providing theoretical convergence guarantees and demonstrating superior empirical performance over existing methods.

Contribution

It generalizes adaptive momentum methods to non-convex min-max problems and establishes convergence rates for this new class of algorithms.

Findings

Proposed algorithm converges at non-asymptotic rates.

Demonstrates superior performance over benchmark methods.

Applicable to a broad class of non-convex min-max problems.

Abstract

Adaptive momentum methods have recently attracted a lot of attention for training of deep neural networks. They use an exponential moving average of past gradients of the objective function to update both search directions and learning rates. However, these methods are not suited for solving min-max optimization problems that arise in training generative adversarial networks. In this paper, we propose an adaptive momentum min-max algorithm that generalizes adaptive momentum methods to the non-convex min-max regime. Further, we establish non-asymptotic rates of convergence for the proposed algorithm when used in a reasonably broad class of non-convex min-max optimization problems. Experimental results illustrate its superior performance vis-a-vis benchmark methods for solving such problems.