Statistical Inference After Adaptive Sampling in Non-Markovian Environments

There is a great desire to use adaptive sampling methods, such as reinforcement learning (RL) and bandit algorithms, for the real-time personalization of interventions in digital applications like mobile health and education. A major obstacle preventing more widespread use of such algorithms in practice is the lack of assurance that the resulting adaptively collected data can be used to reliably answer inferential questions, including questions about time-varying causal effects. Current methods for statistical inference on such data are insufficient because they (a) make strong assumptions regarding the environment dynamics, e.g., assume a contextual bandit or Markovian environment, or (b) require data to be collected with one adaptive sampling algorithm per user, which excludes data collected by algorithms that learn to select actions by pooling the data of multiple users. In this work, we make initial progress by introducing the adaptive sandwich estimator to quantify uncertainty; this estimator (a) is valid even when user rewards and contexts are non-stationary and highly dependent over time, and (b) accommodates settings in which an online adaptive sampling algorithm learns using the data of all users. Furthermore, our inference method is robust to misspecification of the reward models used by the adaptive sampling algorithm. This work is motivated by our work designing experiments in which RL algorithms are used to select actions, yet reliable statistical inference is essential for conducting primary analyses after the trial is over.