Off-policy estimation with adaptively collected data: the power of online learning
Keywords: Causal inference, function approximation, learning theory, off-policy estimation, online learning, reinforcement learning
TL;DR: We provide non-asymptotic guarantees of the AIPW estimator using the framework of online learning for estimation of the treatment effect. We then give a lower bound to demonstrate the instance-optimality of the proposed estimator.
Abstract: We consider estimation of a linear functional of the treatment effect from adaptively collected data. This problem finds a variety of applications including off-policy evaluation in contextual bandits, and estimation of the average treatment effect in causal inference. While a certain class of augmented inverse propensity weighting (AIPW) estimators enjoys desirable asymptotic properties including the semi-parametric efficiency, much less is known about their non-asymptotic theory with adaptively collected data. To fill in the gap, we first present generic upper bounds on the mean-squared error of the class of AIPW estimators that crucially depends on a sequentially weighted error between the treatment effect and its estimates. Motivated by this, we propose a general reduction scheme that allows one to produce a sequence of estimates for the treatment effect via online learning to minimize the sequentially weighted estimation error. To illustrate this, we provide three concrete instantiations in (1) the tabular case; (2) the case of linear function approximation; and (3) the case of general function approximation for the outcome model. We then provide a local minimax lower bound to show the instance-dependent optimality of the AIPW estimator using no-regret online learning algorithms.
Primary Area: Causal inference
Submission Number: 15301
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