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We present a general approach to deriving bounds on the generalization errorof randomized learning algorithms. Our approach can be used to obtain bounds onthe average generalization error as well as bounds on its tail probabilities,both for the case in which a new hypothesis is randomly generated every timethe algorithm is used - as often assumed in the probably approximately correct(PAC)-Bayesian literature - and in the single-draw case, where the hypothesisis extracted only once. For this last scenario, we present a novel bound thatis explicit in the central moments of the information density. The boundreveals that the higher the order of the information density moment that can becontrolled, the milder the dependence of the generalization bound on thedesired confidence level. Furthermore, we use tools from binary hypothesistesting to derive a second bound, which is explicit in the tail of theinformation density. This bound confirms that a fast decay of the tail of theinformation density yields a more favorable dependence of the generalizationbound on the confidence level.

Generalization Error Bounds via $m$th Central Moments of the Information Density