Achieving the Pareto Frontier of Regret Minimization and Best Arm Identification in Multi-Armed Bandits. (arXiv:2110.08627v2 [cs.LG] UPDATED)

We study the Pareto frontier of two archetypal objectives in multi-armed
bandits, namely, regret minimization (RM) and best arm identification (BAI)
with a fixed horizon. It is folklore that the balance between exploitation and
exploration is crucial for both RM and BAI, but exploration is more critical in
achieving the optimal performance for the latter objective. To this end, we
design and analyze the BoBW-lil'UCB$(\gamma)$ algorithm. Complementarily, by
establishing lower bounds on the regret achievable by any algorithm with a …

arm arxiv identification multi-armed bandits