DO-GAN: A DOUBLE ORACLE FRAMEWORK FOR GENERATIVE ADVERSARIAL NETWORKS

Abstract

In this paper, we propose a new approach to train Generative Adversarial Networks (GANs) where we deploy a double-oracle framework using the generator and discriminator oracles. GAN is essentially a two-player zero-sum game between the generator and the discriminator. Training GANs is challenging as a pure Nash equilibrium may not exist and even finding the mixed Nash equilibrium is difficult as GANs have a large-scale strategy space. In DO-GAN, we extend the double oracle framework to GANs. We first generalize the player strategies as the trained models of generator and discriminator from the best response oracles. We then compute the meta-strategies using a linear program. Next, we prune the weaklydominated player strategies to keep the oracles from becoming intractable. We apply our framework to established architectures such as vanilla GAN, Deep Convolutional GAN, Spectral Normalization GAN and Stacked GAN. Finally, we conduct evaluations on MNIST, CIFAR-10 and CelebA datasets and show that DO-GAN variants have significant improvements in both subjective qualitative evaluation and quantitative metrics, compared with their respective GAN architectures.

1. INTRODUCTION

Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) have been applied in various domains such as image and video generation, image-to-image translation and text-to-image synthesis (Liu et al., 2017; Reed et al., 2016) . Various architectures are proposed to generate more realistic samples (Radford et al., 2015; Mirza & Osindero, 2014; Pu et al., 2016) as well as regularization techniques (Arjovsky et al., 2017; Miyato et al., 2018b) . From the game-theoretic perspective, GANs can be viewed as a two-player game where the generator samples the data and the discriminator classifies the data as real or generated. The two networks are alternately trained to maximize their respective utilities until convergence corresponding to a pure Nash Equilibrium (NE). However, pure NE cannot be reliably reached by existing algorithms as pure NE may not exist (Farnia & Ozdaglar, 2020; Mescheder et al., 2017) . This also leads to unstable training in GANs depending on the data and the hyperparameters. Therefore, mixed NE is a more suitable solution concept (Hsieh et al., 2019) . Several recent works propose mixture architectures with multiple generators and discriminators that consider mixed NE such as MIX+GAN (Arora et al., 2017) and MGAN (Hoang et al., 2018) . MIX+GAN and MGAN cannot guarantee to converge to mixed NE. Mirror-GAN (Hsieh et al., 2019) finds the mixed NE by sampling over the infinite-dimensional strategy space and proposes provably convergent proximal methods. However, the sampling approach may not be efficient as mixed NE may only have a few strategies in the support set. Double Oracle (DO) algorithm (McMahan et al., 2003) is a powerful framework to compute mixed NE in large-scale games. The algorithm starts with a restricted game with a small set of actions and solves it to get the NE strategies of the restricted game. The algorithm then computes players' best-responses using oracles to the NE strategies and add them into the restricted game for the next iteration. DO framework has been applied in various disciplines (Jain et al., 2011; Bošanský et al., 2013) , as well as Multi-agent Reinforcement Learning (MARL) settings (Lanctot et al., 2017) . Inspired by the successful applications of DO framework, we, for the first time, propose a Double Oracle Framework for Generative Adversarial Networks (DO-GAN). This paper presents four key contributions. First, we treat the generator and the discriminator as players and obtain the best responses from their oracles and add the utilities to a meta-matrix. Second, we propose a linear

