Introduction
This project develops a new decision-focused learning framework by combining recent advances in the Smart Predict-then-Optimize (SPO) loss with deep neural networks.
While the SPO loss provides a natural way to evaluate predictive models in optimization settings, its non-convexity and non-Lipschitz nature present challenges for both theory and practice. Building on recent progress in establishing generalisation bounds through margin-based relaxations, we extend the framework to deep learning models, offering both improved predictive accuracy and stronger decision guarantees.
Specifically, we would like to first use a deep neural network to predict unknown input parameters of an optimisation problem, and then make decisions by solving the optimisation problem using the predicted parameters. A natural loss function, referred as Smart Predict-then-Optimize (SPO) loss, is to measure the suboptimality of the decisions induced by the predicted input parameters, as opposed to measuring loss using input parameter prediction error. We will develop a tractable methodology for training neural networks under this SPO framework and derive dedicated theoretical garantuees such as consistency results and risk bounds.
The proposed method will be applied to maritime logistics, with a focus on emissions compliance under evolving international regulations. By predicting uncertain factors such as fuel prices, emissions rates, and operational conditions directly through neural networks and integrating them with optimization-based decision models, the project provides a robust tool for analyzing industry responses to policy interventions. The expected outcome is both theoretical—new generalization results for deep learning under SPO loss—and practical, offering evidence-based insights to guide regulators and shipping companies in balancing compliance costs with environmental objectives.
References:
[1] Elmachtoub, A. N., & Grigas, P. (2022). Smart “predict, then optimize”. Management Science.
[2] Liu, H., & Grigas, P. (2021). Risk bounds and calibration for a smart predict-then-optimize method. Advances in Neural Information Processing Systems.
[3] El Balghiti, O., Elmachtoub, A. N., Grigas, P., & Tewari, A. (2019). Generalization bounds in the predict-then-optimize framework. Advances in neural information processing systems.
[4] Wen, J., Abeel, T., & de Weerdt, M. (2025). Performance and interaction assessment of neural network architectures and bivariate smart predict-then-optimize. Machine Learning.