Before revision:  We showcase asymptotic optimality and finite-sample upper bounds on the regret of the  proposed design mechanism . Simulations illustrate the advantage of the method over state-of-art methodologies  .
After revision:  We showcase asymptotic optimality and finite-sample upper bounds on the regret of the first and second wave experiments to guarantee unconfounded experimentation, we showcase tradeoffs in the choice of the pilot's size, and we formally characterize the pilot's size relative to the main experiment. We derive asymptotic properties of estimators of interest under the proposed design mechanism . Simulations illustrate the advantage of the method over state-of-art methodologies .