  Mode estimation is a classical problem in statistics with a wide range of
applications in machine learning. Despite this, there is little understanding
in its robustness properties under possibly adversarial data contamination. In
this paper, we give precise robustness guarantees as well as privacy guarantees
under simple randomization. We then introduce a theory for multi-armed bandits
where the values are the modes of the reward distributions instead of the mean.
We prove regret guarantees for the problems of top arm identification, top
m-arms identification, contextual modal bandits, and infinite continuous arms
top arm recovery. We show in simulations that our algorithms are robust to
perturbation of the arms by adversarial noise sequences, thus rendering modal
bandits an attractive choice in situations where the rewards may have outliers
or adversarial corruptions.
