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.

翻译：多数PAC-Bayesian界限都存在于分批学习环境中,即数据是在推断或预测之前同时收集的。这与收集数据流和算法必须动态调整的许多当代学习问题有些不同。 我们证明在这个在线学习框架中有新的PAC-Bayesian界限,利用最新的遗憾定义,我们重新审视传统的PAC-Bayesian结果,分批逐线转换,将其范围扩大到依赖数据的情况。我们的结果维持着受约束的损失,有可能是\emph{non-convex},为有希望的在线学习发展铺平了道路。