Decision-Making with Unbounded Loss Functions

We consider the problem of decision-making under uncertainty with unbounded loss functions. Inspired by PAC learning model, we 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 system identification and parameter estimation. We address sufficient conditions for consistent decision-making as well as exponential convergence behavior. In this regard, besides a requirement on the growth function of the class of loss functions, it suffices to have a dominating function whose Orlicz expectation is uniformly bounded over the probabilistic model. Decay exponent, decay rate, and sample complexity for expected risk minimization decision policy are discussed, as well