An optimal algorithm for the Thresholding Bandit Problem
This provides the first optimal strategy for a non-trivial pure exploration setting with fixed budget, addressing a specific problem in bandit theory for researchers and practitioners in machine learning.
The paper tackles the Thresholding Bandit Problem, a combinatorial pure exploration stochastic bandit problem where the goal is to identify arms with means above a threshold within a fixed time horizon, and proposes a parameter-free algorithm proven optimal with matching upper and lower bounds.
We study a specific \textit{combinatorial pure exploration stochastic bandit problem} where the learner aims at finding the set of arms whose means are above a given threshold, up to a given precision, and \textit{for a fixed time horizon}. We propose a parameter-free algorithm based on an original heuristic, and prove that it is optimal for this problem by deriving matching upper and lower bounds. To the best of our knowledge, this is the first non-trivial pure exploration setting with \textit{fixed budget} for which optimal strategies are constructed.