ASSISTING THE ADVERSARY TO IMPROVE GAN TRAINING

Abstract

Some of the most popular methods for improving the stability and performance of GANs involve constraining or regularizing the discriminator. In this paper we consider a largely overlooked regularization technique which we refer to as the Adversary's Assistant (AdvAs). We motivate this using a different perspective to that of prior work. Specifically, we consider a common mismatch between theoretical analysis and practice: analysis often assumes that the discriminator reaches its optimum on each iteration. In practice, this is essentially never true, often leading to poor gradient estimates for the generator. To address this, AdvAs is a theoretically motivated penalty imposed on the generator based on the norm of the gradients used to train the discriminator. This encourages the generator to move towards points where the discriminator is optimal. We demonstrate the effect of applying AdvAs to several GAN objectives, datasets and network architectures. The results indicate a reduction in the mismatch between theory and practice and that AdvAs can lead to improvement of GAN training, as measured by FID scores.

1. INTRODUCTION

The generative adversarial network (GAN) framework (Goodfellow et al., 2014) trains a neural network known as a generator which maps from a random vector to an output such as an image. Key to training is another neural network, the adversary (sometimes called a discriminator or critic), which is trained to distinguish between "true" and generated data. This is done by maximizing one of the many different objectives proposed in the literature; see for instance Goodfellow et al. (2014); Arjovsky et al. (2017); Nowozin et al. (2016) . The generator directly competes against the adversary: it is trained to minimize the same objective, which it does by making the generated data more similar to the true data. GANs are efficient to sample from, requiring a single pass through a deep network, and highly flexible, as they do not require an explicit likelihood. They are especially suited to producing photo-realistic images (Zhou et al., 2019) compared to competing methods like normalizing flows, which impose strict requirements on the neural network architecture (Kobyzev et al., 2020; Rezende & Mohamed, 2015) and VAEs (Kingma & Welling, 2014; Razavi et al., 2019; Vahdat & Kautz, 2020) . Counterbalancing their appealing properties, GANs can have unstable training dynamics (Kurach et al., 2019; Goodfellow, 2017; Kodali et al., 2017; Mescheder et al., 2018) . Substantial research effort has been directed towards improving the training of GANs. These endeavors can generally be divided into two camps, albeit with significant overlap. The first develops better learning objectives for the generator/adversary to minimize/maximize. These are designed to have properties which improve training (Arjovsky et al., 2017; Li et al., 2017; Nowozin et al., 2016) . The other camp develops techniques to regularize the adversary and improve its training dynamics (Kodali et al., 2017; Roth et al., 2017; Miyato et al., 2018) . The adversary can then provide a better learning signal for the generator. Despite these contributions, stabilizing the training of GANs remains unsolved and continues to be an active research area. An overlooked approach is to train the generator in a way that accounts for the adversary not being trained to convergence. One such approach was introduced by Mescheder et al. ( 2017) and later built on by Nagarajan & Kolter (2017) . The proposed method is a regularization term based on the norm of the gradients used to train the adversary. This is motivated as a means to improve the convergence properties of the minimax game. The purpose of this paper is to provide a new perspective as to why

