  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.
