Policy Choice and Best Arm Identification: Asymptotic Analysis of Exploration Sampling

Understand

We consider the "policy choice" problem -- otherwise known as best arm identification in the bandit literature -- proposed by Kasy and Sautmann (2021) for adaptive experimental design.

• Theorem 1 of Kasy and Sautmann (2021) provides three asymptotic results that give theoretical guarantees for exploration sampling developed for this setting.
• We first show that the proof of Theorem 1 (1) has technical issues, and the proof and statement of Theorem 1 (2) are incorrect.
• We then show, through a counterexample, that Theorem 1 (3) is false.