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We present two alternative ways to apply PAC-Bayesian analysis to sequencesof dependent random variables. The first is based on a new lemma that enablesto bound expectations of convex functions of certain dependent random variablesby expectations of the same functions of independent Bernoulli randomvariables. This lemma provides an alternative tool to Hoeffding-Azumainequality to bound concentration of martingale values. Our second approach isbased on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis.We also introduce a way to apply PAC-Bayesian analysis in situation of limitedfeedback. We combine the new tools to derive PAC-Bayesian generalization andregret bounds for the multiarmed bandit problem. Although our regret bound isnot yet as tight as state-of-the-art regret bounds based on otherwell-established techniques, our results significantly expand the range ofpotential applications of PAC-Bayesian analysis and introduce a new analysistool to reinforcement learning and many other fields, where martingales andlimited feedback are encountered.

PAC-Bayesian Analysis of Martingales and Multiarmed Bandits