  We develop a new framework for designing online policies given access to an
oracle providing statistical information about an offline benchmark. Having
access to such prediction oracles enables simple and natural Bayesian selection
policies, and raises the question as to how these policies perform in different
settings.
  Our work makes two important contributions towards this question: First, we
develop a general technique we call *compensated coupling* which can be used to
derive bounds on the expected regret (i.e., additive loss with respect to a
benchmark) for any online policy and offline benchmark. Second, using this
technique, we show that a natural greedy policy, which we call *the Bayes
Selector*, has constant expected regret (i.e., independent of the number of
arrivals and resource levels) for a large class of problems we refer to as
Online Allocation with finite types, which includes widely-studied Online
Packing and Online Matching problems. Our results generalize and simplify
several existing results for Online Packing and Online Matching, and suggest a
promising pathway for obtaining oracle-driven policies for other online
decision-making settings.
