Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. Our results show that a very small number of batches gives close to minimax optimal...

A modern, decision-theoretic framework can help clarify important practical questions of experimental design. Building on our recent work, this chapter begins by summarizing our framework for understanding the goals of experimenters, and applying this to re-randomization.We then use this...