Reviews: Semi-Parametric Efficient Policy Learning with Continuous Actions

This paper considers the off-policy learning problem for the case of continuous treatments, and provides regret bounds for the doubly-robust estimator, as well as study of semiparametric efficiency. The primary assumptions are that the "value function" is of known parametric form in the treatment, but with arbitrary dependence on covariates. The proposed approach for continuous treatments avoids the unfavorable dimension dependence of previous approaches for continuous treatments, instead the difficulty is in the matrix regression problem of the covariance-based generalization of the propensity score for the continuous case. Quality: The paper is technically sound with claims well supported by theoretical analysis. Clarity: The paper is overall clear but sometimes vague in descriptions.