Prior-Dependent Allocations for Bayesian Fixed-Budget Best-Arm Identification in Structured Bandits

Best arm identification (BAI) addresses the challenge of finding the optimal arm in a bandit environment (Lattimore and Szepesvári, 2020), with wide-ranging applications in online advertising, drug discovery or hyperparameter tuning. BAI is commonly approached through two primary paradigms: fixed-confidence and fixed-budget. In the fixed-confidence setting (Even-Dar et al., 2006; Kaufmann et al., 2016), the objective is to find the optimal arm with a pre-specified confidence level. Conversely, fixed-budget BAI (Audibert et al., 2010; Karnin et al., 2013; Carpentier and Locatelli, 2016) involves identifying the optimal arm within a fixed number of observations. Within this fixed-budget context, two main metrics are used: the probability of error (PoE) (Audibert et al., 2010; Karnin et al., 2013; Carpentier and Locatelli, 2016)--the likelihood of incorrectly identifying the optimal arm--and the simple regret (Bubeck et al., 2009; Russo, 2016; Komiyama et al., 2023)--the expected performance disparity between the chosen and the optimal arm.