Experimenting on Markov Decision Processes with Local Treatments

Utilizing randomized experiments to evaluate the effect of short-term treatments on the short-term outcomes has been well understood and become the golden standard in industrial practice. However, as service systems become increasingly dynamical and personalized, much focus is shifting toward maximizing long-term cumulative outcomes, such as customer lifetime value, through lifetime exposure to interventions. To bridge this gap, we investigate the randomized experiments within dynamical systems modeled as Markov Decision Processes (MDPs). Our goal is to assess the impact of treatment and control policies on long-term cumulative rewards from relatively short-term observations. We first develop optimal inference techniques for assessing the effects of general treatment patterns. Furthermore, recognizing that many real-world treatments tend to be fine-grained and localized for practical efficiency and operational convenience, we then propose methods to harness this localized structure by sharing information on the non-targeted states. Our new estimator effectively overcomes the variance lower bound for general treatments while matching the more stringent lower bound incorporating the local treatment structure. Furthermore, our estimator can optimally achieve a linear reduction with the number of test arms for a major part of the variance. Finally, we explore scenarios with perfect knowledge of the control arm and design estimators that further improve inference efficiency.