  This note describes the optimal policy rule, according to the local
asymptotic minimax regret criterion, for best arm identification when there are
only two treatments. It is shown that the optimal sampling rule is the Neyman
allocation, which allocates a constant fraction of units to each treatment in a
manner that is proportional to the standard deviation of the treatment
outcomes. When the variances are equal, the optimal ratio is one-half. This
policy is independent of the data, so there is no adaptation to previous
outcomes. At the end of the experiment, the policy maker adopts the treatment
with higher average outcomes.
