Adaptive A/B Testing under Nonstationary Dynamics using State-Space Models

A/B testing is central to evaluating how modifications to products, services, and user experiences impact user outcomes. Yet in practice, experiments rarely occur in stationary environments: seasonality, feature launches, and dynamically evolved user demographics make the underlying treatment effects shift over time. Conventional fixed-allocation designs fail to adapt to this nonstationarity, relying on static treatment allocations that potentially compromise estimation efficiency and lead to inefficient use of experimental resources. Response-adaptive randomization (RAR) design provides a natural alternative, adaptively allocating participants over time based on accrued information. In this work, we propose a methodology framework that addresses these challenges. On the one hand, we model period-level treatment arm means as autoregressive state-space processes and develop a Kalman smoother estimator for the time-averaged treatment effect that exploits temporal dependence. On the other hand, we propose an RAR design that accommodates nonstationarity by incorporating state uncertainty via predicted Kalman variances. Our theoretical analysis establishes asymptotic normality of both a naive and a smoother-based estimator, proves that the smoother strictly dominates the naive estimator in asymptotic variance under correct specification, compares relative efficiency, and enables the construction of anytime-valid confidence sequences for continuous monitoring. Simulation studies demonstrate that our method is significantly more efficient than a benchmark time-averaging estimator and fixed allocation strategy, particularly under treatment effect drift and variance imbalance.