Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition
(2026)
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- 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 La-grangian 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 par-allelization. In particular, it consistently outper-forms 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.
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Citations
Way, S. E.-C., Percot, H., Cappart, Q., Guns, T., & Rousseau, L.-M. (2026). Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition. IJCAI-ECAI 2026 Accepted Papers, #3743. https://hdl.handle.net/2078.5/277776 (Original work published 2026)