Adaptive Experimental Design using Shrinkage Estimators (Evan Rosenman, Claremont McKenna College)
September 14 @ 4:15 pm - 5:15 pm
In multi-armed trials, adaptive designs are a popular way to increase estimation efficiency or identify optimal treatments. Many recent papers have proposed adaptive methods for minimizing the error of unbiased estimators that consider each treatment arm in isolation. This approach may be inefficient, because it fails to borrow shared information across the treatment arms.
We consider adaptivity in a sequential trial with K active treatments and a control, and suggest the use of Stein-like shrinkage estimators to obtain the final causal estimates. These estimators share information, yielding reductions in expected estimation error, relative to estimating each causal effect in isolation. Moreover, for a group of candidate estimators, the expected error can be expressed as the expectation of ratios of Gaussian quadratic forms, and can thus be computed efficiently. Hence, we suggest a simple algorithm for sequential adaptivity: assign each new arrival to the arm that will minimize the estimated shrinker loss.
Through simulations, we demonstrate that this approach reduces estimation error, especially in the low signal-to-noise regime. We also characterize how our adaptive algorithm assigns treatments differently than would a classical Neyman allocation and suggest a method for constructing shorter confidence intervals at the conclusion of the trial.
