Open Problem: Optimal Best Arm Identification with Fixed Budget
This is an incremental discussion of an open problem in bandit theory, relevant for researchers in machine learning and optimization.
The paper addresses the open problem of determining the asymptotic complexity for best arm identification in the fixed-budget setting, noting that while the fixed-confidence setting is well-understood, little is known about its dual.
Best arm identification or pure exploration problems have received much attention in the COLT community since Bubeck et al. (2009) and Audibert et al. (2010). For any bandit instance with a unique best arm, its asymptotic complexity in the so-called fixed-confidence setting has been completely characterized in Garivier and Kaufmann (2016) and Chernoff (1959), while little is known about the asymptotic complexity in its "dual" setting called fixed-budget setting. This note discusses the open problems and conjectures about the instance-dependent asymptotic complexity in the fixed-budget setting.