Decision-Aware Utility Learning for Assortment Optimization

We study assortment optimization under multinomial logit (MNL) choice models from a decision-aware perspective. Classical approaches first estimate a choice model and then optimize an assortment under the estimated model. However, lower estimation error does not necessarily translate into better assortment decisions. We therefore train the choice model directly using the downstream revenue loss. The resulting problem has a discrete lower-level assortment problem and a non-smooth bilevel structure. By exploiting revenue-ordered optimality, we characterize the selected assortment by a threshold. The original exponential formulation admits a mixed-integer exponential-conic relaxation, whose computational cost grows rapidly with the numbers of products and training scenarios. We then introduce a linearized variant and derive an equivalent mixed-integer linear program, substantially improving computational scalability. To mitigate decision-equivalent solutions arising from the pure decision-aware objective, we further introduce a probability-fitting regularization. Numerical experiments show that the decision-aware approach is particularly effective in data-scarce settings and when model misspecification materially affects downstream decisions.