Non-stationary Experimental Design under Linear Trends

Experimentation has been critical and increasingly popular across various domains, such as clinical trials and online platforms, due to its widely recognized benefits. One of the primary objectives of classical experiments is to estimate the average treatment effect (ATE) to inform future decision-making. However, in healthcare and many other settings, treatment effects may be non-stationary, meaning that they can change over time, rendering the traditional experimental design inadequate and the classical static ATE uninformative. In this work, we address the problem of non-stationary experimental design under linear trends by considering two objectives: estimating the dynamic treatment effect and minimizing welfare loss within the experiment. We propose an efficient design that can be customized for optimal estimation error rate, optimal regret rate, or the Pareto optimal trade-off between the two objectives. We establish information-theoretical lower bounds that highlight the inherent challenge in estimating dynamic treatment effects and minimizing welfare loss, and also statistically reveal the fundamental trade-off between them.