The field of Contextual Optimization (CO) integrates machine learning and optimization to solve decision making problems under uncertainty. Recently, a risk sensitive variant of CO, known as Conditional Robust Optimization (CRO), combines uncertainty quantification with robust optimization in order to promote safety and reliability in high stake applications. Exploiting modern differentiable optimization methods, we propose a novel end-to-end approach to train a CRO model in a way that accounts for both the empirical risk of the prescribed decisions and the quality of conditional coverage of the contextual uncertainty set that supports them. While guarantees of success for the latter objective are impossible to obtain from the point of view of conformal prediction theory, high quality conditional coverage is achieved empirically by ingeniously employing a logistic regression differentiable layer within the calculation of coverage quality in our training loss.We show that the proposed training algorithms produce decisions that outperform the traditional estimate then optimize approaches.

In this paper, we study a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Specifically, we solve this problem from a Conditional Robust Optimization (CRO) point of view. We propose an integrated framework that designs the conditional uncertainty set by jointly learning the partitions in the covariate data space and simultaneously constructing partition specific deep uncertainty sets for the random vector that perturbs the CRO problem. We also provide theoretical guarantees for the coverage of the uncertainty sets and value at risk performances obtained using the proposed CRO approach. Finally, we use the simulated and real world data to show the implementation of our approach and compare it against two non-contextual benchmark approaches to demonstrate the value of exploiting contextual information in robust optimization.

Product brands employ shopper marketing (SM) strategies to convert shoppers along the path to purchase. Traditional marketing mix models (MMMs), which leverage regression techniques and historical data, can be used to predict the component of sales lift due to SM tactics. The resulting predictive model is a critical input to plan future SM strategies. The implementation of traditional MMMs, however, requires significant ad-hoc manual intervention due to their limited flexibility in (i) explicitly capturing the temporal link between decisions; (ii) accounting for the interaction between business rules and past (sales and decision) data during the attribution of lift to SM; and (iii) ensuring that future decisions adhere to business rules. These issues necessitate MMMs with tailored structures for specific products and retailers, each requiring significant hand-engineering to achieve satisfactory performance -- a major implementation challenge. We propose an SM Optimization and Inverse Learning Engine (SMOILE) that combines optimization and inverse reinforcement learning to streamline implementation. SMOILE learns a model of lift by viewing SM tactic choice as a sequential process, leverages inverse reinforcement learning to explicitly couple sales and decision data, and employs an optimization approach to handle a wide-array of business rules. Using a unique dataset containing sales and SM spend information across retailers and products, we illustrate how SMOILE standardizes the use of data to prescribe future SM decisions. We also track an industry benchmark to showcase the importance of encoding SM lift and decision structures to mitigate spurious results when uncovering the impact of SM decisions.