  We introduce a novel framework for the estimation of the posterior
distribution over the weights of a neural network, based on a new probabilistic
interpretation of adaptive optimisation algorithms such as AdaGrad and Adam. We
demonstrate the effectiveness of our Bayesian Adam method, Badam, by
experimentally showing that the learnt uncertainties correctly relate to the
weights' predictive capabilities by weight pruning. We also demonstrate the
quality of the derived uncertainty measures by comparing the performance of
Badam to standard methods in a Thompson sampling setting for multi-armed
bandits, where good uncertainty measures are required for an agent to balance
exploration and exploitation.
