PAC-Bayes under potentially heavy tails

WederivePAC-Bayesian learning guarantees forheavy-tailed losses, andobtain a novel optimal Gibbs posterior which enjoys finite-sample excess risk bounds atlogarithmic confidence. Ourcoretechnique itselfmakesuseofPAC-Bayesian inequalities in order to derive a robust risk estimator, which by design is easy to compute.