Faster Rates for Policy Learning Alexander R. Luedtke 1,2 and Antoine Chambaz 3,4 1 Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, USA $^{2}$Public Health Sciences Division, Fred Hutchinson Cancer Research Center, USA $^{3}$Modal’X, UPL, Univ Paris Nanterre, F92000 Nanterre France $^{4}$Division of Biostatistics, School of Public Health, UC Berkeley, USA This article improves the existing proven rates of regret decay in optimal policy estimation. We give a margin-free result showing that the regret decay for estimating a within-class optimal policy is second-order for empirical risk minimizers over Donsker classes, with regret decaying at a faster rate than the standard error of an efficient estimator of the value of an optimal policy. We also give a result from the classification literature that shows that faster regret decay is possible via plug-in estimation provided a margin condition holds. Four examples are considered. In these examples, the regret is expressed in terms of either the mean value or the median value; the number of possible actions is either two or finitely many; and the sampling scheme is either independent and identically distributed or sequential, where the latter represents a contextual bandit sampling scheme. Keywords: individualized treatment rules; personalized medicine; policy learning; precision medicine 1 Abstract arXiv:1704.06431v1 [math.ST] 21 Apr 2017