On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach
This addresses a key bottleneck in training sequential games like GANs, though it is an incremental improvement over existing minimax optimization algorithms.
The paper tackles the problem of naive gradient descent failing to find local minimax points in minimax optimization by proposing the Follow-the-Ridge algorithm, which provably converges only to local minimax and improves GAN training convergence compared to recent methods.
Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is tempting to apply gradient descent to solve minimax optimization given its popularity and success in supervised learning. However, it has been noted that naive application of gradient descent fails to find some local minimax and can converge to non-local-minimax points. In this paper, we propose \emph{Follow-the-Ridge} (FR), a novel algorithm that provably converges to and only converges to local minimax. We show theoretically that the algorithm addresses the notorious rotational behaviour of gradient dynamics, and is compatible with preconditioning and \emph{positive} momentum. Empirically, FR solves toy minimax problems and improves the convergence of GAN training compared to the recent minimax optimization algorithms.