Post Reinforcement Learning Inference

Abstract: We consider estimation and inference using data collected from reinforcement learning algorithms. These algorithms, characterized by their adaptive experimentation, interact with individual units over multiple stages, dynamically adjusting their strategies based on previous interactions. Our goal is to evaluate a counterfactual policy post-data collection and estimate structural parameters, like dynamic treatment effects, which can be used for credit assignment and determining the effect of earlier actions on final outcomes. Such parameters of interest can be framed as solutions to moment equations, but not minimizers of a population loss function, leading to Z-estimation approaches for static data. However, in the adaptive data collection environment of reinforcement learning, where algorithms deploy nonstationary behavior policies, standard estimators do not achieve asymptotic normality due to the fluctuating variance. We propose a weighted Z-estimation approach with carefully designed adaptive weights to stabilize the time-varying estimation variance. We identify proper weighting schemes to restore the consistency and asymptotic normality of the weighted Z-estimators for target parameters, which allows for hypothesis testing and constructing uniform confidence regions. Primary applications include dynamic treatment effect estimation and dynamic off-policy evaluation.