to [1] for a recent overview of the literature. Exciting developments in policy learning over the last several years include outcome weighted learning [2, 3, 4], ensemble techniques [5], and empirical risk minimizers (ERMs) [1], to name a few. Each of these works has established some form of regret bound for the estimator, with most of these regret rates slower than n − 1 / $^{2}$. Notable exceptions to this n − 1 / 2 restriction occur for outcome weighted learning (OWL) methods under a hard margin [2] and rates attainable by plug-in estimation strategies [6, 7, 8]. We give our results in Section 2. Our first result pertains to empirical risk minimization within a Donsker class, where the optimal policy is defined as the so-called “value” maximizer within this class. These estimators were recently studied in [1], and were also discussed for continuous treatments in [9]. The second result links the optimal policy problem to the classification literature, which has shown that faster regret decay rates are attainable by plug-in estimators under certain margin conditions [10]. Section 3 gives three remarks, one relating our results to the pioneering results of Koltchinskii [11], another studying which term in our regret bound dominates the rate, and the third relating our results to those of Athey and Wager [1]. Section A proves our results regarding empirical risk minimization. All of our results are for the regret under a fixed data generating distribution. The fast rate that we will establish for ERMs (independent of any margin assumption) will not transfer to the minimax setting unless some form of margin assumption is imposed. We do not give high probability results, though these are often a straightforward extension of convergence in probability results when working within Donsker classes. Throughout this work, when we refer to Donsker classes, we are referring to P -Donsker classes, where P is the data generating distribution, rather than universal/uniform Donsker classes [12]. While our ERM results are not useful for non- P -Donsker classes, we note that they also serve as an oracle guarantee for an ensemble procedure, such as [5], so that one need not know in advance whether or not all of the classes over which they are optimizing are P -Donsker for the result to be useful. 3