Online PAC-Bayes Learning

Maxime Haddouche, Benjamin Guedj

Keywords: PAC-Bayes, Online Learning, Non-Convex losses

TL;DR: We prove new PAC-Bayesian bounds in the online learning framework, and we revisit classical results with a batch-to-online conversion, for non-convex losses.

Abstract: Most PAC-Bayesian bounds hold in the batch learning setting where data is collected at once, prior to inference or prediction. This somewhat departs from many contemporary learning problems where data streams are collected and the algorithms must dynamically adjust. We prove new PAC-Bayesian bounds in this online learning framework, leveraging an updated definition of regret, and we revisit classical PAC-Bayesian results with a batch-to-online conversion, extending their remit to the case of dependent data. Our results hold for bounded losses, potentially \emph{non-convex}, paving the way to promising developments in online learning.