Online PAC-Bayes Learning
This work addresses the gap in theoretical guarantees for online learning algorithms, particularly for non-convex problems, which is incremental but relevant for streaming data applications.
The paper tackles the problem of extending PAC-Bayesian bounds from batch to online learning with dependent data, proving new bounds for non-convex losses and enabling dynamic algorithm adjustments.
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.