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We propose a novel knowledge distillation (KD) method to selectively instill teacher knowledge into a student model motivated by situations where the student’s capacity is significantly smaller than that of the teachers. In vanilla KD, the teacher primarily sets a predictive target for the student to follow, and we posit that this target is overly optimistic due to the student’s lack of capacity. We develop a novel scaffolding scheme where the teacher, in addition to setting a predictive target, also scaffolds the student’s prediction by censoring hard-to-learn examples. The student model utilizes the same information as the teacher’s soft-max predictions as inputs, and in this sense, our proposal can be viewed as a natural variant of vanilla KD. We show on synthetic examples that censoring hard-examples leads to smoothening the student’s loss landscape so that the student encounters fewer local minima. As a result, it has good generalization properties. Against vanilla KD, we achieve improved performance and are comparable to more intrusive techniques that leverage feature matching on benchmark datasets. 

We consider the classical problem of multi-class prediction with expert advice, but with an active learning twist. In this new setting the learner will only query the labels of a small number of examples, but still aims to minimize regret to the best expert as usual; the learner is also allowed a very short "burn-in" phase where it can fast-forward and query certain highly-informative examples. We design an algorithm that utilizes Hedge (aka Exponential Weights) as a subroutine, and we show that under a very particular combinatorial constraint on the matrix of expert predictions we can obtain a very strong regret guarantee while querying very few labels. This constraint, which we refer to as ζ -compactness, or just compactness, can be viewed as a non-stochastic variant of the disagreement coefficient, another popular parameter used to reason about the sample complexity of active learning in the IID setting. We also give a polynomial-time algorithm to calculate the ζ -compactness of a matrix up to an approximation factor of 3.