Discriminative Bayesian filtering lends momentum to the stochastic Newton method for minimizing log-convex functions

• URL: http://arxiv.org/abs/2104.12949v3
• Date: Mon, 21 Aug 2023 14:44:30 GMT
• Title: Discriminative Bayesian filtering lends momentum to the stochastic Newton method for minimizing log-convex functions
• Authors: Michael C. Burkhart
• Abstract summary: We show how the Newton method iteratively updates its estimate using subsampled versions of gradient and Hessian versions. Applying Bayesian filtering, we consider the entire history of observations. We establish matrix-based conditions under which the effect of older observations diminishes. We illustrate various aspects of our approach with an example and other innovations for the Newton method.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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