Adaptive Neyman Allocation in Sequential Trials: An Online Optimization Perspective

Oregon Convention Center 

In this talk, I present our recent work on the problem of Adaptive Neyman Allocation, where the experimenter seeks to construct an adaptive design which is nearly as efficient as the optimal (but infeasible) non-adaptive Neyman design which has access to all potential outcomes. I will show that the experimental design problem is equivalent to an adversarial online convex optimization problem, suggesting that any solution must exhibit some amount of algorithmic sophistication. Next, I present Clip-OGD, an experimental design that combines the online gradient descent principle with a new time-varying probability-clipping technique. I will show that the Neyman variance is attained in large samples by showing that the expected regret of the online optimization problem is bounded by O(\sqrt{T}), up to sub-polynomial factors. Even though the design is adaptive, we construct a consistent (conservative) estimator for the variance, which facilitates the development of valid confidence intervals. I will conclude with recent progress on extending this work to covariate-adjusted estimators and covariate-responsive designs, which is made possible through the online optimization perspective.