Variational Inference with Tail-adaptive f-Divergence

Abstract: Variational inference with {\alpha}-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using {\alpha}-divergences (with positive {\alpha} values) is their mass-covering property. However, estimating and optimizing {\alpha}-divergences require to use importance sampling, which could have extremely large or infinite variances due to heavy tails of importance weights. In this paper, we propose a new class of tail-adaptive f-divergences that adaptively change the convex function f with the tail of the importance weights, in a way that theoretically guarantees finite moments, while simultaneously achieving mass-covering properties. We test our methods on Bayesian neural networks, as well as deep reinforcement learning in which our method is applied to improve a recent soft actor-critic (SAC) algorithm. Our results show that our approach yields significant advantages compared with existing methods based on classical KL and {\alpha}-divergences.