Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantile Multi-Armed Bandits: Optimal Best-Arm Identification and a
  Differentially Private Scheme   We study the best-arm identification problem in multi-armed bandits with
stochastic, potentially private rewards, when the goal is to identify the arm
with the highest quantile at a fixed, prescribed level. First, we propose a
(non-private) successive elimination algorithm for strictly optimal best-arm
identification, we show that our algorithm is $\delta$-PAC and we characterize
its sample complexity. Further, we provide a lower bound on the expected number
of pulls, showing that the proposed algorithm is essentially optimal up to
logarithmic factors. Both upper and lower complexity bounds depend on a special
definition of the associated suboptimality gap, designed in particular for the
quantile bandit problem, as we show when the gap approaches zero, best-arm
identification is impossible. Second, motivated by applications where the
rewards are private, we provide a differentially private successive elimination
algorithm whose sample complexity is finite even for distributions with
infinite support-size, and we characterize its sample complexity. Our
algorithms do not require prior knowledge of either the suboptimality gap or
other statistical information related to the bandit problem at hand.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con