Standard experimental designs are geared toward point estimation and hypothesis testing, while bandit algorithms are geared toward in‐sample outcomes. Here, we instead consider treatment assignment in an experiment with several waves for choosing the best among a set of possible policies (treatments) at the end of the experiment. We propose a computationally tractable assignment algorithm that we call “exploration sampling,” where assignment probabilities in each wave are an increasing concave function of the posterior probabilities that each treatment is optimal. We prove an asymptotic optimality result for this algorithm and demonstrate improvements in welfare in calibrated simulations over both non‐adaptive designs and bandit algorithms. An application to selecting between six different recruitment strategies for an agricultural extension service in India demonstrates practical feasibility.