Distributionally Robust Games: Wasserstein Metric

Deep generative models are powerful but difficult to train due to its instability, saturation problem and high dimensional data distribution. This paper introduces a game theory framework with Wasserstein metric to train generative models, in which the unknown data distribution is learned by dynamically optimizing the worst-case payoff. In the game, two types of players work on opposite objectives to solve a minimax problem. The defenders explore the Wasserstein neighborhood of real data to generate a set of hard samples which have the maximum distance from the model distribution. The attackers update the model to fit for the hard set so as to minimize the discrepancy between model and data distributions. Instead of Kullback-Leibler divergence, we use Wasserstein distance to measure the similarity between distributions. The Wasserstein metric is a true distance with better topology in the parameter space, which improves the stability of training. We provide practical algorithms to train deep generative models, in which an encoder network is designed to learn the feature vector of the high dimensional data. The algorithm is tested on CelebA human face dataset and compared with the state-of-the-art generative models. Performance evaluation shows the training process is stable and converges fast. Our model can produce visual pleasing images which are closer to the real distribution in terms of Wasserstein distance.