Title: Bootstrap Robust Prescriptive Analytics,
Abstract: We address the problem of prescribing an optimal decision in a framework
where its cost depends on uncertain problem parameters $Y$ that need to be
learned from data. Earlier work by Bertsimas and Kallus (2014) transforms
classical machine learning methods that merely predict $Y$ from supervised
training data $[(x_1, y_1), \dots, (x_n, y_n)]$ into prescriptive methods
taking optimal decisions specific to a particular covariate context $X=\bar x$.
Their prescriptive methods factor in additional observed contextual information
on a potentially large number of covariates $X=\bar x$ to take context specific
actions $z(\bar x)$ which are superior to any static decision $z$. Any naive
use of limited training data may, however, lead to gullible decisions
over-calibrated to one particular data set. In this paper, we borrow ideas from
distributionally robust optimization and the statistical bootstrap of Efron
(1982) to propose two novel prescriptive methods based on (nw) Nadaraya-Watson
and (nn) nearest-neighbors learning which safeguard against overfitting and
lead to improved out-of-sample performance. Both resulting robust prescriptive
methods reduce to tractable convex optimization problems and enjoy a limited
disappointment on bootstrap data. We illustrate the data-driven decision-making
framework and our novel robustness notion on a small news vendor problem as
well as a small portfolio allocation problem.