Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: <lb>We study the best arm identification (Best-1-Arm) problem, which is defined as follows.<lb>We are given n stochastic bandit arms. The ith arm has a reward distribution<lb>Di with an<lb>unknown mean μi. Upon each play of the ith arm, we can get a reward, sampled i.i.d. from<lb>Di. We would like to identify the arm with the largest mean with probability at least 1 − δ,<lb>using as few samples as possible. We provide a nontrivial algorithm for Best-1-Arm, which<lb>improves upon several prior upper bounds on the same problem. We also study an important<lb>special case where there are only two arms, which we call the Sign-ξ problem. We provide a<lb>new lower bound of Sign-ξ, simplifying and significantly extending a classical result by Farrell<lb>in 1964, with a completely new proof. Using the new lower bound for Sign-ξ, we obtain the<lb>first lower bound for Best-1-Arm that goes beyond the classic Mannor-Tsitsiklis lower bound,<lb>by an interesting reduction from Sign-ξ to Best-1-Arm. We propose an interesting conjecture<lb>concerning the optimal sample complexity of Best-1-Arm from the perspective of instance-wise<lb>optimality.

On the Optimal Sample Complexity for Best Arm Identification