{"type":"ScholarlyArticle","title":"Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition","authors":[{"name":"Stéphane Eilles-Chan Way","slug":"stephane-eilles-chan-way","given":"Stéphane","family":"Eilles-Chan Way","affiliation":""},{"name":"Hugo Percot","slug":"hugo-percot","given":"Hugo","family":"Percot","affiliation":""},{"name":"Quentin Cappart","slug":"quentin-cappart","given":"Quentin","family":"Cappart","affiliation":""},{"name":"Tias Guns","slug":"tias-guns","given":"Tias","family":"Guns","affiliation":""},{"name":"Louis-Martin Rousseau","slug":"louis-martin-rousseau","given":"Louis-Martin","family":"Rousseau","affiliation":""}],"abstract":"Decision-focused learning has shown great promise for addressing predict-then-optimize problems, particularly in the presence of under-specified models. However, its practical deployment is often hindered by high computational costs and limited scalability, as it requires solving a constrained optimization problem for each training instance at every iteration. To address these challenges, we propose a novel framework that incorporates Lagrangian decomposition into the decision-focused learning paradigm. Specifically, we introduce a new surrogate objective along with two loss functions for evaluating and training the underlying prediction model. We further propose two variants of our approach, which offer different trade-offs between computational efficiency and solution quality. Our framework can be seamlessly integrated with standard decision-focused learning methods, including Smart Predict-then-Optimize (SPO+) and Implicit Maximum Likelihood Estimation (IMLE). Through experiments on two standard benchmarks, the multi-dimensional knapsack problem and quadratic portfolio optimization, we demonstrate that our approach achieves competitive performance while remaining amenable to parallelization. In particular, it consistently outperforms traditional decision-focused learning methods  on large-scale instances, involving up to eight times more variables than those typically considered in related work. The implementation is available at https://github.com/corail-research/DFL-LD.","doi":"10.24963/ijcai.2026/247","url":"https://ijcai.org/proceedings/2026/247","pdf":"https://ijcai.org/proceedings/2026/0247.pdf","markdown":"https://ijcai.org/proceedings/2026/247.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/247","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":247,"pages":{"first":2217,"last":2226},"keywords":["Constraint Satisfaction and Optimization: Constraint optimization problems","Constraint Satisfaction and Optimization: Other"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}