Partial Monitoring with Side Information

In a partial-monitoring problem in every round a learner chooses an action, simultaneously an opponent chooses an outcome, then the learner suffers some loss and receives some feedback. The goal of the learner is to minimize his (unobserved) cumulative loss. In this paper we explore a variant of this problem where in every round, before the learner makes his decision, he receives some side-information. We assume that the outcomes are generated randomly from a distribution that is influenced by the side-information. We present a “meta” algorithm scheme that reduces the problem to that of the construction of an algorithm that is able to estimate the distributions of observations while producing confidence bounds for these estimates. Two specific examples are shown for such estimators: One uses linear estimates, the other uses multinomial logistic regression. In both cases the resulting algorithm is shown to achieve Õ( √ T ) minimax regret for locally observable partial-monitoring games.