Title: Noisy Natural Gradient as Variational Inference,
Abstract: Variational Bayesian neural nets combine the flexibility of deep learning
with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff
between cheap but simple variational families (e.g.~fully factorized) or
expensive and complicated inference procedures. We show that natural gradient
ascent with adaptive weight noise implicitly fits a variational posterior to
maximize the evidence lower bound (ELBO). This insight allows us to train
full-covariance, fully factorized, or matrix-variate Gaussian variational
posteriors using noisy versions of natural gradient, Adam, and K-FAC,
respectively, making it possible to scale up to modern-size ConvNets. On
standard regression benchmarks, our noisy K-FAC algorithm makes better
predictions and matches Hamiltonian Monte Carlo's predictive variances better
than existing methods. Its improved uncertainty estimates lead to more
efficient exploration in active learning, and intrinsic motivation for
reinforcement learning.