Variational Inference with Tail-adaptive f-Divergence

By Dilin Wang, Hao Liu, Qiang Liu. 2018

61 citations recorded by the source corpus.

Variational inference with α-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using α-divergences (with positive α values) is their mass-covering property. However, estimating and optimizing α-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 guarantee 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 (Haarnoja et al., 2018). Our results show that our approach yields significant advantages compared with existing methods based on classical KL and α-divergences.

Subfields: Artificial Intelligence, Control and Systems Engineering, Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Evgenii Egorov
2. Evgeny Burnaev
3. Ruslan Kostoev
4. Kirill Neklyudov

In Probabilistic & Bayesian Methods

1. Evgenii Egorov
2. Evgeny Burnaev
3. Ruslan Kostoev
4. Kirill Neklyudov

Citations in the corpus

• AUTO-ENCODING VARIATIONAL BAYES (2020, unknown): “Tail adaptive algorithms [48] might help to select the best performing Rènyi divergence.”
• MaxEntropy Pursuit Variational Inference (2019, methodology): “Using Taylor expansion we can get the approximation for any f -divergence [27] by the Pearson Chi-squared divergence:”