This paper considers the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, the authors use a slightly different model that incorporates the notion of side information in a more generic form to make it applicable to a broader class of applications including parameter estimation and system identification. The paper addresses sufficient conditions for consistent decision-making with exponential convergence behavior. In this regard, besides a certain condition on the growth function of the class of loss functions, it suffices that the class of loss functions be dominated by a measurable function whose exponential Orlicz expectation is uniformly bounded over the probabilistic model.
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