TRAINING FEDERATED GANS WITH THEORETICAL GUARANTEES: A UNIVERSAL AGGREGATION APPROACH

Abstract

Recently, Generative Adversarial Networks (GANs) have demonstrated their potential in federated learning, i.e., learning a centralized model from data privately hosted by multiple sites. A federated GAN jointly trains a centralized generator and multiple private discriminators hosted at different sites. A major theoretical challenge for the federated GAN is the heterogeneity of the local data distributions. Traditional approaches cannot guarantee to learn the target distribution, which is a mixture of the highly different local distributions. This paper tackles this theoretical challenge, and for the first time, provides a provably correct framework for federated GAN. We propose a new approach called Universal Aggregation, which simulates a centralized discriminator via carefully aggregating the mixture of all private discriminators. We prove that a generator trained with this simulated centralized discriminator can learn the desired target distribution. Through synthetic and real datasets, we show that our method can learn the mixture of largely different distributions where existing federated GAN methods fail.

1. INTRODUCTION

Generative Adversarial Networks (GANs) have attracted much attention due to their ability to generate realistic-looking synthetic data (Goodfellow et al., 2014; Zhang et al., 2018; Liu et al., 2019b; Shaham et al., 2019; Dai et al., 2017; Kumar et al., 2017) . In order to obtain a powerful GAN model, one needs to use data with a wide range of characteristics (Qi, 2019) . However, these diverse data are often owned by different sources, and to acquire their data is often infeasible. For instance, most hospitals and research institutions are unable to share data with the research community, due to privacy concerns (Annas et al., 2003; Mercuri, 2004; lex, 2014; Gostin et al., 2009) and government regulations (Kerikmäe, 2017; Seddon & Currie, 2013) . To circumvent the barrier of data sharing for GAN training, one may resort to Federated Learning (FL), a promising new decentralized learning paradigm (McMahan et al., 2017) . In FL, one trains a centralized model but only exchanges model information with different data sources. Since the central model has no direct access to data at each source, privacy concerns are alleviated (Yang et al., 2019; Kairouz et al., 2019) . This opens the opportunity for a federated GAN, i.e., a centralized generator with multiple local and privately hosted discriminators (Hardy et al., 2019) . Each local discriminator is only trained on its local data and provides feedback to the generator w.r.t. synthesized data (e.g., gradient). A federated GAN empowers GAN with much more diversified data without violating privacy constraints. Despite the promises, a convincing approach for training a federated GAN remains unknown. The major challenge comes from the non-identical local distributions from multiple data sources/entities. The centralized generator is supposed to learn a mixture of these local distributions from different entities, whereas each discriminator is only trained on local data and learns one of the local distributions. The algorithm and theoretical guarantee of traditional single-discriminator GAN (Goodfellow et al., 2014) do not easily generalize to this federated setting. A federated GAN should integrate feedback from local discriminators in an intelligent way, so that the generator can 'correctly' learn the mixture distribution. Directly averaging feedbacks from local discriminators (Hardy et al., 2019) results in a strong bias toward common patternsowever, such non-identical distribution setting is classical in federated learning (Zhao et al., 2018; Smith et al., 2017; Qu et al., 2020) and characteristic of local data improves the diversity of data.

