  To minimize the average of a set of log-convex functions, the stochastic
Newton method iteratively updates its estimate using subsampled versions of the
full objective's gradient and Hessian. We contextualize this optimization
problem as sequential Bayesian inference on a latent state-space model with a
discriminatively-specified observation process. Applying Bayesian filtering
then yields a novel optimization algorithm that considers the entire history of
gradients and Hessians when forming an update. We establish matrix-based
conditions under which the effect of older observations diminishes over time,
in a manner analogous to Polyak's heavy ball momentum. We illustrate various
aspects of our approach with an example and review other relevant innovations
for the stochastic Newton method.
