We formulate stochastic gradient descent (SGD) as a novel factorised Bayesian filtering problem, in which each parameter is inferred separately, conditioned on the corresopnding backpropagated gradient.   Inference in this setting naturally gives rise to BRMSprop and BAdam: Bayesian variants of RMSprop and Adam.   Remarkably, the Bayesian approach recovers many features of state-of-the-art adaptive SGD methods, including amongst others root-mean-square normalization, Nesterov acceleration and AdamW.  As such, the Bayesian approach provides one explanation for the empirical effectiveness of state-of-the-art adaptive SGD algorithms.   Empirically comparing BRMSprop and BAdam with naive RMSprop and Adam on MNIST, we find that Bayesian methods have the potential to considerably reduce test loss and classification error.
We formulated SGD as a Bayesian filtering problem, and show that this gives rise to RMSprop, Adam, AdamW, NAG and other features of state-of-the-art adaptive methods The paper analyzes stochastic gradient descent through Bayesian filtering as a framework for analyzing adaptive methods. The authors attempt to unify existing adaptive gradient methods under the Bayesian filtering framework with the dynamical prior