Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition

• URL: http://arxiv.org/abs/2606.08797v1
• Date: Sun, 07 Jun 2026 19:27:59 GMT
• Title: Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition
• Abstract summary: Decision-focused learning has shown great promise for addressing predict-then-optimize problems.<n>It requires solving a constrained optimization problem for each training instance at every iteration.<n>We propose a novel framework that incorporates Lagrangian decomposition into the decision-focused learning paradigm.
• Score: 8.22941091333064
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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