Bayesian Learning via Neural Schr\"odinger-F\"ollmer Flows

TL;DR

This paper introduces a novel Bayesian inference framework using neural Schrödinger-Föllmer flows, leveraging stochastic control to provide a finite-time, low-variance alternative to traditional methods like SGLD, with theoretical guarantees and connections to existing variational inference routines.

Contribution

It proposes a new stochastic control-based approach for Bayesian inference that improves upon existing methods in terms of variance and finite-time guarantees.

Findings

Framework offers low-variance, finite-time Bayesian inference.

Connections established between stochastic control and variational inference.

Theoretical guarantees adapted for the proposed method.

Abstract

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr\"odinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics (SGLD). Furthermore, we discuss and adapt the existing theoretical guarantees of this framework and establish connections to already existing VI routines in SDE-based models.