  The combination of lightly supervised pre-training and online fine-tuning has
played a key role in recent AI developments. These new learning pipelines call
for new theoretical frameworks. In this paper, we formalize core aspects of
weakly supervised and active learning with a simple problem: the estimation of
the mode of a distribution using partial feedback. We show how entropy coding
allows for optimal information acquisition from partial feedback, develop
coarse sufficient statistics for mode identification, and adapt bandit
algorithms to our new setting. Finally, we combine those contributions into a
statistically and computationally efficient solution to our problem.
