Optimizing Adaptive Experiments: A Unified Approach to Regret
  Minimization and Best-Arm Identification
Chao Qin Daniel Russo
Practitioners conducting adaptive experiments often encounter two competing
priorities: reducing the cost of experimentation by effectively assigning
treatments during the experiment itself, and gathering information swiftly to
conclude the experiment and implement a treatment across the population.
Currently, the literature is divided, with studies on regret minimization
addressing the former priority in isolation, and research on best-arm
identification focusing solely on the latter. This paper proposes a unified
model that accounts for both within-experiment performance and post-experiment
outcomes. We then provide a sharp theory of optimal performance in large
populations that unifies canonical results in the literature. This unification
also uncovers novel insights. For example, the theory reveals that familiar
algorithms, like the recently proposed top-two Thompson sampling algorithm, can
be adapted to optimize a broad class of objectives by simply adjusting a single
scalar parameter. In addition, the theory reveals that enormous reductions in
experiment duration can sometimes be achieved with minimal impact on both
within-experiment and post-experiment regret.