WA4 - Integration of Machine Learning and Optimization

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and leverage them to solve downstream problems, for example risk-averse formulations. We focus on human choice settings that can be formulated as (integer) linear programs. In such settings, existing inverse optimization and choice modelling methods infer preferences from observed choices but typically produce point estimates or fail to capture contextual shifts, making them unsuitable for risk-averse decision-making. Using a bounded-variance score function gradient estimator, we train a predictive model mapping contextual features to a rich class of parameterizable distributions. This approach yields a maximum likelihood estimate. The model generates scenarios for unseen contexts in the subsequent optimization phase. In a synthetic ridesharing environment, our approach reduces average post-decision surprise by up to 114x compared to a risk-neutral approach with perfect predictions and up to 25x compared to leading risk-averse baselines.

Many decision-making problems, from fire suppression to transportation, involve endogenous uncertainty. The standard predict-then-optimize pipeline estimates a model and optimizes accordingly, often ignoring how prediction errors affect decisions. Decision-focused learning instead optimizes predictions for decision quality, offering improved robustness and stochastic dominance. However, it is computationally demanding and limited for decision-dependent settings. We propose a tractable decision-focused approach for such problems.

Data-driven optimization is increasingly used in high-stakes decision-making, yet their solutions are often difficult to interpret. This challenge is particularly acute in contextual stochastic optimization, where decisions depend on features that also shape uncertainty.
In this talk, we address the problem of computing relative counterfactual explanations in contextual optimization problems under decision-dependent uncertainty. The approach identifies minimal changes in contextual features that enable alternative decisions while maintaining controlled performance guarantees. We illustrate the approach on a facility location problem subject to decision-dependent demand distributions and discuss both practical and computational insights.

In this paper, we propose a novel ML-based approach for solving two-stage stochastic programs (2SP) by learning the objective coefficients of a surrogate master problem. We design two training losses: an imitation-based loss and an objective-based loss, corresponding to supervised and self-supervised learning, respectively. Both losses require differentiating the first-stage solution with respect to the input. The objective-based loss is particularly attractive because it circumvents the need to generate labels for first-stage decisions. However, it requires embedding the second-stage problem as an additional layer in the neural network, and differentiating the second-stage objective with respect to the first-stage solution in the backward pass. We show that, under mild conditions, this gradient can be obtained “for free.” Finally, we validate our approach on the stochastic capacitated facility location problem (SCFLP) and the simultaneous stochastic optimization of mining complexes (SSOMC).