Belief Flows of Robust Online Learning

TL;DR

This paper presents a probabilistic online learning model that uses Gaussian beliefs and flow-based updates, combining Bayesian principles with gradient evaluations for efficient and robust learning in classification tasks.

Contribution

It introduces a novel belief flow framework that integrates stochastic gradients with information-theoretic updates for online learning.

Findings

Outperforms traditional online algorithms in classification tasks

Demonstrates robustness and efficiency in neural network training

Provides a new perspective on probabilistic belief updates

Abstract

This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian belief over the optimal weight parameters. Unlike traditional Bayesian updates, the model incorporates a small number of gradient evaluations at locations chosen using Thompson sampling, making it computationally tractable. The belief is then transformed via a linear flow field which optimally updates the belief distribution using rules derived from information theoretic principles. Several versions of the algorithm are shown using different constraints on the flow field and compared with conventional online learning algorithms. Results are given for several classification tasks including logistic regression and multilayer neural networks.