Primary Submission Category: Design of Experiments
Adaptive Experimental Design Using Shrinkage Estimators
Authors: Evan Rosenman, Kristen Hunter,
Presenting Author: Evan Rosenman*
In multi-armed trials, adaptive designs are widely used to improve estimation efficiency, identify optimal treatments, or maximize rewards. Recent studies have explored using adaptive trials to achieve better simultaneous estimates of the effects of K active treatments relative to a control arm. One approach is to employ either batch or sequential variants of Neyman allocation, typically using Horvitz-Thompson-style estimators to produce causal estimates at the trial’s conclusion. However, this approach may be inefficient in that it fails to borrow information across the treatment arms.
In this paper, we consider adaptivity when using a Stein-like shrinkage estimator for heteroscedastic data to estimate the causal effects in multi-arm trials. This estimator pools information across treatment effect estimates, provably reducing the expected squared error loss compared to independent estimation of treatment effects. We demonstrate that the expected loss can be expressed as a Gaussian quadratic form, enabling efficient computation via numerical integration. This result paves the way for sequential adaptivity, allowing treatments to be assigned to minimize the shrinker loss. Through simulations, we demonstrate that this approach can yield meaningful reductions in estimation error and characterize how our adaptive algorithm assigns treatments differently than would a sequential Neyman allocation.