Abstract

We discuss an online learning framework in which the agent is allowed to say “I don’t know” as well as making incorrect predictions on given examples. We analyze the trade off between saying “I don’t know” and making mistakes. If the number of don’t-know predictions is required to be zero, the model reduces to the well-known mistake-bound model introduced by Littlestone [Lit88]. On the other hand, if no mistakes are allowed, the model reduces to KWIK framework introduced by Li et. al. [LLW08]. We propose a general, though inefficient, algorithm for general finite concept classes that minimizes the number of don’t-know predictions subject to a given bound on the number of allowed mistakes. We then present specific polynomial-time algorithms for the concept classes of monotone disjunctions and linear separators with a margin.