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

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.