🤖 AI Summary
Switchback experiments suffer from causal estimation bias and diminished statistical power due to carryover effects, limiting their reliability in tech industry applications. To address this, we propose the first minimax-optimal switchback design framework. We establish a finite-population central limit theorem enabling conservative hypothesis testing and valid confidence interval construction. Furthermore, we develop a data-driven method for identifying the order of carryover effects. Technically, our approach integrates discrete optimization, continuous relaxation, randomization-based inference, and explicit carryover effect modeling, with rigorous analysis of model misspecification impacts. Simulation studies demonstrate strong robustness across diverse carryover structures, substantial gains in statistical power, and improved inferential robustness. The methodology has been operationalized into a production-ready experimental design and analysis guideline deployable in real-world A/B testing platforms.
📝 Abstract
Switchback experiments, where a firm sequentially exposes an experimental unit to random treatments, are among the most prevalent designs used in the technology sector, with applications ranging from ride-hailing platforms to online marketplaces. Although practitioners have widely adopted this technique, the derivation of the optimal design has been elusive, hindering practitioners from drawing valid causal conclusions with enough statistical power. We address this limitation by deriving the optimal design of switchback experiments under a range of different assumptions on the order of the carryover effect—the length of time a treatment persists in impacting the outcome. We cast the optimal experimental design problem as a minimax discrete optimization problem, identify the worst-case adversarial strategy, establish structural results, and solve the reduced problem via a continuous relaxation. For switchback experiments conducted under the optimal design, we provide two approaches for performing inference. The first provides exact randomization-based p-values, and the second uses a new finite population central limit theorem to conduct conservative hypothesis tests and build confidence intervals. We further provide theoretical results when the order of the carryover effect is misspecified and provide a data-driven procedure to identify the order of the carryover effect. We conduct extensive simulations to study the numerical performance and empirical properties of our results and conclude with practical suggestions. This paper was accepted by George Shanthikumar, big data analytics.
