Generative Adversarial Networks (GAN) (, 2014) are an effective method for training generative models of complex data such as natural images. However, they are notoriously hard to train and can suffer from the problem of missing modes where the model is not able to produce examples in certain regions of the space. We propose an iterative procedure, called AdaGAN, where at every step we add a new component into a mixture model by running a GAN algorithm on a reweighted sample. This is inspired by boosting algorithms, where many potentially weak individual predictors are greedily aggregated to form a strong composite predictor. We prove that such an incremental procedure leads to convergence to the true distribution in a finite number of steps if each step is optimal, and convergence at an exponential rate otherwise. We also illustrate experimentally that this procedure addresses the problem of missing modes.
Rosset and Segal @cite_8 proposed to use an additive mixture model in the case where the log likelihood can be computed. They derived the update rule via computing the steepest descent direction when adding a component with infinitesimal weight. This leads to an update rule which is degenerate if the generative model can produce arbitrarily concentrated distributions (indeed the optimal component is just a Dirac distribution) which is thus not suitable for the GAN setting. Moreover, their results do not apply once the weight @math becomes non-infinitesimal. In contrast, for any fixed weight of the new component our approach gives the overall optimal update (rather than just the best direction), and applies to any @math -divergence. Remarkably, in both theories, improvements of the mixture are guaranteed only if the new weak'' learner is still good enough (see Conditions &)
@cite_8
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Several authors have suggested viewing boosting as a gradient descent search for a good fit in function space. We apply gradient-based boosting methodology to the unsupervised learning problem of density estimation. We show convergence properties of the algorithm and prove that a strength of weak learnability property applies to this problem as well. We illustrate the potential of this approach through experiments with boosting Bayesian networks to learn density models.