Adaptive divergence for rapid adversarial optimization

Abstract

Adversarial Optimization provides a reliable, practical way to match two implicitly defined distributions, one of which is typically represented by a sample of real data, and the other is represented by a parameterized generator. Matching of the distributions is achieved by minimizing a divergence between these distribution, and estimation of the divergence involves a secondary optimization task, which, typically, requires training a model to discriminate between these distributions. The choice of the model has its trade-off: high-capacity models provide good estimations of the divergence, but, generally, require large sample sizes to be properly trained. In contrast, low-capacity models tend to require fewer samples for training; however, they might provide biased estimations. Computational costs of Adversarial Optimization becomes significant when sampling from the generator is expensive. One of the practical examples of such settings is fine-tuning parameters of complex computer simulations. In this work, we introduce a novel family of divergences that enables faster optimization convergence measured by the number of samples drawn from the generator. The variation of the underlying discriminator model capacity during optimization leads to a significant speed-up. The proposed divergence family suggests using low-capacity models to compare distant distributions (typically, at early optimization steps), and the capacity gradually grows as the distributions become closer to each other. Thus, it allows for a significant acceleration of the initial stages of optimization. This acceleration was demonstrated on two fine-tuning problems involving Pythia event generator and two of the most popular black-box optimization algorithms: Bayesian Optimization and Variational Optimization. Experiments show that, given the same budget, adaptive divergences yield results up to an order of magnitude closer to the optimum than Jensen-Shannon divergence. While we consider physics-related simulations, adaptive divergences can be applied to any stochastic simulation.