Utsav Sadana

Utsav Sadana, Abhilash Chenreddy, Erick Delage et al.

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty. This gave rise to the field of contextual optimization, under which data-driven procedures are developed to prescribe actions to the decision-maker that make the best use of the most recently updated information. A large variety of models and methods have been presented in both OR and ML literature under a variety of names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict/estimate-then-optimize, decision-focused learning, (task-based) end-to-end learning/forecasting/optimization, etc. Focusing on single and two-stage stochastic programming problems, this review article identifies three main frameworks for learning policies from data and discusses their strengths and limitations. We present the existing models and methods under a uniform notation and terminology and classify them according to the three main frameworks identified. Our objective with this survey is to both strengthen the general understanding of this active field of research and stimulate further theoretical and algorithmic advancements in integrating ML and stochastic programming.

Utsav Sadana, Erick Delage, Angelos Georghiou

The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data are limited, the empirical entropic risk estimator, formed by replacing the expectation in the risk measure with a sample average, underestimates true risk. We show that this negative bias grows superlinearly with the standard deviation of the loss for distributions with unbounded right tails. We further demonstrate that several existing bias reduction techniques developed for empirical risk either continue to underestimate entropic risk or substantially overestimate it, potentially leading to overly risky or overly conservative decisions. To address this issue, we develop a parametric bootstrap procedure that is strongly asymptotically consistent and provides a controlled overestimation of entropic risk under mild assumptions. The method first fits a distribution to the data and then estimates the empirical estimator's bias via bootstrapping. We show that the fitted distribution must satisfy only weak regularity conditions, and Gaussian mixture models offer a convenient and flexible choice within this class. As an application, we introduce a distributionally robust optimization model for an insurance contract design problem that incorporates correlations in household losses. We show that selecting regularization parameters using standard cross-validation can lead to substantially higher out-of-sample risk for the insurer if the validation bias is not corrected. Our approach improves performance by recommending higher and more accurate premiums, thereby better reflecting the underlying tail risk.