Academic Paper attributes
Experimental design is crucial in evidence-based decision-making with multiple treatment arms, such as online advertisements and medical treatments. This study investigates the problem of identifying the treatment arm with the highest expected outcome, referred to as the best treatment arm, while minimizing the probability of misidentification. This problem has been studied across numerous research fields, including best arm identification (BAI) and ordinal optimization. In our experiments, the number of treatment-allocation rounds is fixed. During each round, a decision-maker allocates a treatment arm to an experimental unit and observes a corresponding outcome, which follows a Gaussian distribution with variances that can differ among the treatment arms. At the end of the experiment, we recommend one of the treatment arms as an estimate of the best treatment arm based on the observations. To design an experiment, we first discuss the worst-case lower bound for the probability of misidentification through an information-theoretic approach. Then, under the assumption that the variances are known, we propose the Generalized-Neyman-Allocation (GNA)-empirical-best-arm (EBA) strategy, an extension of the Neyman allocation proposed by Neyman (1934). We show that the GNA-EBA strategy is asymptotically optimal in the sense that its probability of misidentification aligns with the lower bounds as the sample size increases indefinitely and the differences between the expected outcomes of the best and other suboptimal arms converge to a uniform value. We refer to such strategies as asymptotically worst-case optimal.
