A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately. We propose three optimal allocation strategies in a dynamic setting where treatments are sequentially assigned over time. These strategies are designed to minimize the variance of the treatment effect estimator when data follow a non Markov decision process or a (time-varying) Markov decision process. We further develop estimation procedures based on existing off-policy evaluation (OPE) methods and conduct extensive experiments in various environments to demonstrate the effectiveness of the proposed methodologies. In theory, we prove the optimality of the proposed treatment allocation design and establish upper bounds for the mean squared errors of the resulting treatment effect estimators.

Artificial intelligence systems are trained combining various observational and experimental datasets from different source sites, and are increasingly used to reason about the effectiveness of candidate policies. One common assumption in this context is that the data in source and target sites (where the candidate policy is due to be deployed) come from the same distribution. This assumption is often violated in practice, causing challenges for generalization, transportability, or external validity. Despite recent advances for determining the identifiability of the effectiveness of policies in a target domain, there are still challenges for the accurate estimation of effects from finite samples. In this paper, we develop novel graphical criteria and estimators for evaluating the effectiveness of policies (e.g., conditional, stochastic) by combining data from multiple experimental studies.

A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately. We propose three optimal allocation strategies in a dynamic setting where treatments are sequentially assigned over time. These strategies are designed to minimize the variance of the treatment effect estimator when data follow a non Markov decision process or a (time-varying) Markov decision process. We further develop estimation procedures based on existing off-policy evaluation (OPE) methods and conduct extensive experiments in various environments to demonstrate the effectiveness of the proposed methodologies.

We thank the opportunity offered by editors for this discussion and the discussants for their insightful comments and thoughtful contributions. We also want to congratulate Kallus (2020) for his inspiring work in improving the efficiency of policy learning by retargeting. Motivated from the discussion in Dukes and Vansteelandt (2020), we first point out interesting connections and distinctions between our work and Kallus (2020) in Section 1. In particular, the assumptions and sources of variation for consideration in these two papers lead to different research problems with different scopes and focuses. In Section 2, following the discussions in Li et al. (2020); Liang and Zhao (2020), we also consider the efficient policy evaluation problem when we have some data from the testing distribution available at the training stage. We show that under the assumption that the sample sizes from training and testing are growing in the same order, efficient value function estimates can deliver competitive performance. We further show some connections of these estimates with existing literature. However, when the growth of testing sample size available for training is in a slower order, efficient value function estimates may not perform well anymore. In contrast, the requirement of the testing sample size for DRITR is not as strong as that of efficient policy evaluation using the combined data. Finally, we highlight the general applicability and usefulness of DRITR in Section 3.