Unifying Variational Inference and PAC-Bayes for Supervised Learning that Scales

TL;DR

This paper introduces a scalable method combining variational inference and PAC-Bayes frameworks to improve generalization in high-dimensional neural network controllers, validated on MuJoCo tasks.

Contribution

It unifies variational inference and PAC-Bayes for scalable, high-dimensional supervised learning without explicit environmental assumptions.

Findings

Better generalization in high-dimensional tasks

Theoretical validation of the combined approach

Effective on MuJoCo locomotion benchmarks

Abstract

Neural Network based controllers hold enormous potential to learn complex, high-dimensional functions. However, they are prone to overfitting and unwarranted extrapolations. PAC Bayes is a generalized framework which is more resistant to overfitting and that yields performance bounds that hold with arbitrarily high probability even on the unjustified extrapolations. However, optimizing to learn such a function and a bound is intractable for complex tasks. In this work, we propose a method to simultaneously learn such a function and estimate performance bounds that scale organically to high-dimensions, non-linear environments without making any explicit assumptions about the environment. We build our approach on a parallel that we draw between the formulations called ELBO and PAC Bayes when the risk metric is negative log likelihood. Through our experiments on multiple high dimensional MuJoCo locomotion tasks, we validate the correctness of our theory, show its ability to generalize better, and investigate the factors that are important for its learning. The code for all the experiments is available at https://bit.ly/2qv0JjA.