Simpler PAC-Bayesian bounds for hostile data.

Pierre Alquier, Benjamin Guedj

Abstract: PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution $$\rho $$ ρ to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distribution $$\pi $$ π . Unfortunately, most of the available bounds typically rely on heavy assumptions such as boundedness and independence of the observations. This paper aims at relaxing these constraints and provides PAC-Bayesian learning bounds that hold for dependent, heavy-tailed observations (hereafter referred to as hostile data). In these bounds the Kullack-Leibler divergence is replaced with a general version of Csiszár’s f-divergence. We prove a general PAC-Bayesian bound, and show how to use it in various hostile settings.