A survey of contextual optimization methods for decision-making under uncertainty

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. This survey article unifies these models under the lens of contextual stochastic optimization, thus providing a general presentation of a large variety of problems. We identify three main frameworks for learning policies from data and present the existing models and methods under a uniform notation and terminology. 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.