Conjugate Gradient Method for Generative Adversarial Networks

TL;DR

This paper introduces a conjugate gradient method for training GANs, providing convergence guarantees and demonstrating improved performance over traditional optimizers like SGD and Adam in generating high-quality images.

Contribution

It proposes a novel conjugate gradient approach for solving the local Nash equilibrium in GAN training, with theoretical convergence analysis and empirical performance improvements.

Findings

Converges to local Nash equilibrium under mild assumptions.

Outperforms SGD and momentum SGD in FID scores.

Performs better than Adam on average in experiments.

Abstract

One of the training strategies of generative models is to minimize the Jensen--Shannon divergence between the model distribution and the data distribution. Since data distribution is unknown, generative adversarial networks (GANs) formulate this problem as a game between two models, a generator and a discriminator. The training can be formulated in the context of game theory and the local Nash equilibrium (LNE). It does not seem feasible to derive guarantees of stability or optimality for the existing methods. This optimization problem is far more challenging than the single objective setting. Here, we use the conjugate gradient method to reliably and efficiently solve the LNE problem in GANs. We give a proof and convergence analysis under mild assumptions showing that the proposed method converges to a LNE with three different learning rate update rules, including a constant learning rate. Finally, we demonstrate that the proposed method outperforms stochastic gradient descent (SGD) and momentum SGD in terms of best Frechet inception distance (FID) score and outperforms Adam on average. The code is available at \url{https://github.com/Hiroki11x/ConjugateGradient_GAN}.