From Predictive to Prescriptive Analytics
  In this paper, we combine ideas from machine learning (ML) and operations research and management science (OR/MS) in developing a framework, along with specific methods, for using data to prescribe optimal decisions in OR/MS problems. In a departure from other work on data-driven optimization and reflecting our practical experience with the data available in applications of OR/MS, we consider data consisting, not only of observations of quantities with direct effect on costs/revenues, such as demand or returns, but predominantly of observations of associated auxiliary quantities. The main problem of interest is a conditional stochastic optimization problem, given imperfect observations, where the joint probability distributions that specify the problem are unknown. We demonstrate that our proposed solution methods, which are inspired by ML methods such as local regression, CART, and random forests, are generally applicable to a wide range of decision problems. We prove that they are tractable and asymptotically optimal even when data is not iid and may be censored. We extend this to the case where decision variables may directly affect uncertainty in unknown ways, such as pricing's effect on demand. As an analogue to R^2, we develop a metric P termed the coefficient of prescriptiveness to measure the prescriptive content of data and the efficacy of a policy from an operations perspective. To demonstrate the power of our approach in a real-world setting we study an inventory management problem faced by the distribution arm of an international media conglomerate, which ships an average of 1bil units per year. We leverage internal data and public online data harvested from IMDb, Rotten Tomatoes, and Google to prescribe operational decisions that outperform baseline measures. Specifically, the data we collect, leveraged by our methods, accounts for an 88\% improvement as measured by our P. 
Dimitris Bertsimas, Nathan Kallus
stat.ML cs.LG math.OC