Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
We will consider several multi armed bandit problems (MAB), with a focus on structured, pure exploration bandit problems. We will first identify the minimax rate for the Thresholding Bandit Problem (TBP). We will then go on to consider the TBP under several shape constraints and again classify the minimax rate in each of these cases. The second part of this talk, will be to study the shape constrained TBP in a problem dependent setting. For the TBP, under both a monotone and concave constraint, we will describe problem dependent upper and lower bounds, matching up to log terms. Finally we will consider a potentially infinite armed formulation of the MAB, where a proportion of the arms are optimal. In this setting, we will describe problem dependent upper and lower bounds, matching up to log terms, for both cumulative regret and best arm identification.
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