In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. Theteacher adjusts herteaching method fordifferent students, and the student, after getting familiar with the teacher's instruction mechanism,caninfertheteacher'sintentiontolearnfaster.

We propose the first reduction-based approach to obtaining long-term memory guarantees for online learning in the sense of Bousquet and Warmuth[8], by reducing the problem to achieving typical switching regret.

We will add more discussion on this in the next version of our paper, as suggested by the reviewer. For the full16 information setting, as far as we know there is no existing lower bound. Weare not aware of any25 existing results for tracking asmall set ofexperts with stochastic losses.

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Quitesurprisingly, we show that the convergence speed of the training loss controls the magnitude of the biasing effect: the slower the convergence, the better the bias.

A prime example is single-cell RNA sequencing (scRNA-seq) data (Figure 1).