Negative Momentum for Improved Game Dynamics

TL;DR

This paper investigates the use of negative momentum in gradient-based methods for differentiable games, demonstrating improved stability and convergence in complex game dynamics like GAN training.

Contribution

It introduces the concept of negative momentum in alternating gradient updates, providing theoretical and empirical evidence of its effectiveness in stabilizing game dynamics.

Findings

Alternating updates are more stable than simultaneous ones.

Negative momentum enables convergence in difficult adversarial problems.

Improved training stability for GANs with negative momentum.

Abstract

Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiable games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial networks (GANs) and actor-critic systems. However, compared to single-objective optimization, game dynamics are more complex and less understood. In this paper, we analyze gradient-based methods with momentum on simple games. We prove that alternating updates are more stable than simultaneous updates. Next, we show both theoretically and empirically that alternating gradient updates with a negative momentum term achieves convergence in a difficult toy adversarial problem, but also on the notoriously difficult to train saturating GANs.