论文标题
PAC-BAYES的概括范围是通过超级马丁的重尾损失的范围
PAC-Bayes Generalisation Bounds for Heavy-Tailed Losses through Supermartingales
论文作者
论文摘要
虽然Pac-Bayes现在是一个既定的轻尾损失学习框架（\ emph {e.g。}，subgaussian或subpentential），但它扩展到重型损失的情况下仍然很大程度上没有教堂，并且近年来引起了人们日益增长的兴趣。在损失函数的有界方差的唯一假设下，我们为重尾损失贡献了Pac-bayes的概括范围。在该假设下，我们从\ citet {kuzborskij2019efron}扩展了先前的结果。我们的主要技术贡献是利用马尔可夫对超级男性的不平等的扩展。我们的证明技术通过为无界的玛格纳莱斯提供界限以及批处理和在线学习的范围，从而统一并扩展了不同的pac-bayesian框架。
While PAC-Bayes is now an established learning framework for light-tailed losses (\emph{e.g.}, subgaussian or subexponential), its extension to the case of heavy-tailed losses remains largely uncharted and has attracted a growing interest in recent years. We contribute PAC-Bayes generalisation bounds for heavy-tailed losses under the sole assumption of bounded variance of the loss function. Under that assumption, we extend previous results from \citet{kuzborskij2019efron}. Our key technical contribution is exploiting an extention of Markov's inequality for supermartingales. Our proof technique unifies and extends different PAC-Bayesian frameworks by providing bounds for unbounded martingales as well as bounds for batch and online learning with heavy-tailed losses.
