This work addresses a new problem of learning generative adversarial networks (GANs) from multiple data collections that are each i) owned separately and privately by different clients and ii) drawn from a non-identical distribution that comprises different classes. Given such multi-client and non-iid data as input, we aim to achieve a distribution involving all the classes input data can belong to, while keeping the data decentralized and private in each client storage. Our key contribution to this end is a new decentralized approach for learning GANs from non-iid data called Forgiver-First Update (F2U), which a) asks clients to train an individual discriminator with their own data and b) updates a generator to fool the most forgiving' discriminators who deem generated samples as the most real. Our theoretical analysis proves that this updating strategy indeed allows the decentralized GAN to learn a generator's distribution with all the input classes as its global optimum based on f-divergence minimization. Moreover, we propose a relaxed version of F2U called Forgiver-First Aggregation (F2A), which adaptively aggregates the discriminators while emphasizing forgiving ones to perform well in practice. Our empirical evaluations with image generation tasks demonstrated the effectiveness of our approach over state-of-the-art decentralized learning methods.
Finally, our work has several limitations. i) Our empirical evaluation is based on a simulation in a single workstation. Practical implementations of the proposed approach as well as other baselines will come with problems of communication, security, and scalability for a large number of clients, as discussed in @cite_2 . ii) Our approach by itself is not designed to resolve common problems observed in GAN training, such as mode collapse and theoretical guarantee for convergence. We still require additional contributions to make GANs perform well in practice. iii) The current formulation can be applied only to standard GANs with a generator and a discriminator. One interesting extension for future work is to deal with various architectures such as conditional GANs @cite_40 @cite_44 @cite_3 @cite_32 @cite_6 and GANs with multiple generators @cite_20 @cite_16 @cite_14 @cite_1 @cite_38 .
@cite_38 @cite_14 @cite_1 @cite_32 @cite_3 @cite_6 @cite_44 @cite_40 @cite_2 @cite_16 @cite_20
2787223504 2962919088 2687693326 2963981733
We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss functions raised by recent work: we show that gradient estimators used in the optimization process for both MMD GANs and Wasserstein GANs are unbiased, but learning a discriminator based on samples leads to biased gradients for the generator parameters. We also discuss the issue of kernel choice for the MMD critic, and characterize the kernel corresponding to the energy distance used for the Cramer GAN critic. Being an integral probability metric, the MMD benefits from training strategies recently developed for Wasserstein GANs. In experiments, the MMD GAN is able to employ a smaller critic network than the Wasserstein GAN, resulting in a simpler and faster-training algorithm with matching performance. We also propose an improved measure of GAN convergence, the Kernel Inception Distance, and show how to use it to dynamically adapt learning rates during GAN training. Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Frechet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark. Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the Frechet Inception Distance'' (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.