
The Influence of Shape Constraints on the Thresholding Bandit Problem
We investigate the stochastic Thresholding Bandit problem (TBP) under se...
read it

An optimal algorithm for the Thresholding Bandit Problem
We study a specific combinatorial pure exploration stochastic bandit pro...
read it

Thresholding Bandit Problem with Both Duels and Pulls
The Thresholding Bandit Problem (TBP) aims to find the set of arms with ...
read it

Sample complexity of partition identification using multiarmed bandits
Given a vector of probability distributions, or arms, each of which can ...
read it

Stochastic bandits with armdependent delays
Significant work has been recently dedicated to the stochastic delayed b...
read it

BestofK Bandits
This paper studies the BestofK Bandit game: At each time the player ch...
read it

Identifying Best Interventions through Online Importance Sampling
Motivated by applications in computational advertising and systems biolo...
read it
Problem Dependent View on Structured Thresholding Bandit Problems
We investigate the problem dependent regime in the stochastic Thresholding Bandit problem (TBP) under several shape constraints. In the TBP, the objective of the learner is to output, at the end of a sequential game, the set of arms whose means are above a given threshold. The vanilla, unstructured, case is already well studied in the literature. Taking K as the number of arms, we consider the case where (i) the sequence of arm's means (μ_k)_k=1^K is monotonically increasing (MTBP) and (ii) the case where (μ_k)_k=1^K is concave (CTBP). We consider both cases in the problem dependent regime and study the probability of error  i.e. the probability to misclassify at least one arm. In the fixed budget setting, we provide upper and lower bounds for the probability of error in both the concave and monotone settings, as well as associated algorithms. In both settings the bounds match in the problem dependent regime up to universal constants in the exponential.
READ FULL TEXT
Comments
There are no comments yet.