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. 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.

Explainable Data-Driven Optimization: From Context to Decision and Back Again

Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learning models in the classification setting, explaining decision pipelines involving learning algorithms remains unaddressed. This lack of interpretability can block the adoption of data-driven solutions as practitioners may not understand or trust the recommended decisions. We bridge this gap by introducing a counterfactual explanation methodology tailored to explain solutions to data-driven problems. We introduce two classes of explanations and develop methods to find nearest explanations of random forest and nearest-neighbor predictors. We demonstrate our approach by explaining key problems in operations management such as inventory management and routing.

Robust Counterfactual Explanations for Random Forests

Counterfactual explanations describe how to modify a feature vector in order to flip the outcome of a trained classifier. Several heuristic and optimal methods have been proposed to generate these explanations. However, the robustness of counterfactual explanations when the classifier is re-trained has yet to be studied. Our goal is to obtain counterfactual explanations for random forests that are robust to algorithmic uncertainty. We study the link between the robustness of ensemble models and the robustness of base learners and frame the generation of robust counterfactual explanations as a chance-constrained optimization problem. We develop a practical method with good empirical performance and provide finite-sample and asymptotic guarantees for simple random forests of stumps. We show that existing methods give surprisingly low robustness: the validity of naive counterfactuals is below $50\%$ on most data sets and can fall to $20\%$ on large problem instances with many features. Even with high plausibility, counterfactual explanations often exhibit low robustness to algorithmic uncertainty. In contrast, our method achieves high robustness with only a small increase in the distance from counterfactual explanations to their initial observations. Furthermore, we highlight the connection between the robustness of counterfactual explanations and the predictive importance of features.