Consider an active learning setting in which a learner has a training set with few labeled examples and a pool set with many unlabeled inputs, while a remote teacher has a pre-trained model that is known to perform well for the learner's task. The learner actively transmits batches of unlabeled inputs to the teacher through a constrained communication channel for labeling. This paper addresses the following key questions: (i) Active batch selection: Which batch of inputs should be sent to the teacher to acquire the most useful information and thus reduce the number of required communication rounds? (ii) Batch encoding: How do we encode the batch of inputs for transmission to the teacher to reduce the communication resources required at each round? We introduce Communication-Constrained Bayesian Active Knowledge Distillation (CC-BAKD), a novel protocol that integrates Bayesian active learning with compression via a linear mix-up mechanism. Bayesian active learning selects the batch of inputs based on their epistemic uncertainty, addressing the "confirmation bias" that is known to increase the number of required communication rounds. Furthermore, the proposed mix-up compression strategy is integrated with the epistemic uncertainty-based active batch selection process to reduce the communication overhead per communication round.

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