In statistical learning theory, risk bounds are typically obtained via the manipulation of suprema of empirical processes measuring the largest deviation of the empirical risk from the true risk in a class of models. In this talk we describe the alternative approach of deriving risk bounds for the ensemble of hypotheses obtained by running an arbitrary learning algorithm in an-on line fashion. This allows us to replace the uniform large deviation argument with a simpler argument based on the analysis of the empirical process engendered by the on-line learner. The large deviations of such empirical processes are easily controlled by a single application of Bernstein's inequality for martingales, and the resulting risk bounds exhibit strong data-dependence.