  We consider the best-arm identification problem in multi-armed bandits, which
focuses purely on exploration. A player is given a fixed budget to explore a
finite set of arms, and the rewards of each arm are drawn independently from a
fixed, unknown distribution. The player aims to identify the arm with the
largest expected reward. We propose a general framework to unify sequential
elimination algorithms, where the arms are dismissed iteratively until a unique
arm is left. Our analysis reveals a novel performance measure expressed in
terms of the sampling mechanism and number of eliminated arms at each round.
Based on this result, we develop an algorithm that divides the budget according
to a nonlinear function of remaining arms at each round. We provide theoretical
guarantees for the algorithm, characterizing the suitable nonlinearity for
different problem environments described by the number of competitive arms.
Matching the theoretical results, our experiments show that the nonlinear
algorithm outperforms the state-of-the-art. We finally study the
side-observation model, where pulling an arm reveals the rewards of its related
arms, and we establish improved theoretical guarantees in the pure-exploration
setting.
