Adaptive Experimental Design Using Shrinkage Estimators

2026-02-07

AI Summary

This study addresses the inefficiency of conventional adaptive designs—such as sequential Neyman allocation—in multi-arm randomized trials, which arises from estimating treatment effects in isolation. The authors introduce, for the first time, a Stein-type shrinkage estimator into adaptive experimental design, leveraging information sharing across treatment arms to improve the precision of causal effect estimates under heteroscedasticity. The proposed method dynamically optimizes individual allocation strategies by exploiting a computable expression for the expected loss based on Gaussian quadratic forms. Both theoretical analysis and simulation experiments demonstrate that this approach substantially reduces estimation error and yields allocation patterns distinct from those of traditional schemes, thereby overcoming a key bottleneck in information utilization inherent in existing adaptive designs.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Causal Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In the setting of multi-armed trials, adaptive designs are a popular way to increase estimation efficiency, identify optimal treatments, or maximize rewards to individuals. Recent work has considered the case of estimating the effects of K active treatments, relative to a control arm, in a sequential trial. Several papers have proposed sequential versions of the classical Neyman allocation scheme to assign treatments as individuals arrive, typically with the goal of using Horvitz-Thompson-style estimators to obtain causal estimates at the end of the trial. However, this approach may be inefficient in that it fails to borrow information across the treatment arms. In this paper, we consider adaptivity when the final causal estimation is obtained using a Stein-like shrinkage estimator for heteroscedastic data. Such an estimator shares information across treatment effect estimates, providing provable reductions in expected squared error loss relative to estimating each causal effect in isolation. Moreover, we show that the expected loss of the shrinkage estimator takes the form of a Gaussian quadratic form, allowing it to be computed efficiently using 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. We also characterize how our adaptive algorithm assigns treatments differently than would a sequential Neyman allocation.

Problem

• adaptive experimental design
• shrinkage estimator
• multi-armed trials
• causal estimation
• treatment allocation

Innovation

• shrinkage estimator
• adaptive experimental design
• multi-armed trials
• causal inference
• Stein estimation