From Predictive to Prescriptive Analytics

By Dimitris J. Bertsimas, Nathan Kallus. 2014

722 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Learning When-to-Treat Policies (2019, methodology): “…data to help inform how and to whom interventions should be applied (Manski 2004; Zhang et al. 2012; Zhao et al. 2012; Dudík et al. 2014; Swaminathan and Joachims 2015; Elmachtoub and Grigas 2017; Kallus and Zhou 2018; Kitagawa and Tetenov 2018; Athey and Wager 2020; Bertsimas and Kallus 2020).”
Strong mixed-integer programming formulations for trained neural networks (2018, background): “Broadly, our work fits into a growing body of research in prescriptive analytics and specifically the “predict, then optimize” framework, which considers how to embed trained machine learning models into optimization problems [11,12,17,18,24,28,39].”
Prescriptive analytics: Literature review and research challenges (2020, neutral): “Although prediction evaluation algorithms have gathered recent research attention, it is not clear how to go from a good prediction to a good decision (Bertsimas & Kallus, 2014), since prescriptive analytics algorithms incorporate additional uncertainty sources in information processing.”
Market Segmentation Trees (2019, methodology): “Bertsimas and Kallus (2020), Cui et al. (2018), Ferreira et al. (2016), Glaeser et al. (2019), and Nambiar et al. (2019) use regression tree ensembles (e.g., bagging, boosting, or random forests) to predict demand in retail settings.”
Optimal trees for prediction and prescription (2018, background): “More generally in the fields of operations research and management science, Bertsimas and Kallus [11] consider the problem of prescribing optimal decisions by directly learning from data.”
Policy Learning With Observational Data (2017, result): “From this perspective, our result is related to the work of Ban and Rudin (2019) and Bertsimas and Kallus (2020), who study data-driven rules for optimal inventory management and related problems.”
Decision Trees for Decision-Making under the Predict-then-Optimize Framework (2020, positive): “Bertsimas and Kallus (2019) show how to properly leverage ML algorithms, including decision trees, in order to yield asymptotically optimal decisions to a class of stochastic optimization problems.”
Optimization Models for Machine Learning: A Survey (2019, background): “Thus methodological developments that can leverage data predictions for optimal decision making is an area of research that is critical for future business value [29, 142, 167].”