Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition

Researchers propose a novel framework combining Lagrangian decomposition with decision-focused learning to improve scalability and computational efficiency in predict-then-optimize problems. The approach demonstrates competitive performance on large-scale benchmarks with up to 8x more variables than previous methods, while maintaining parallelization capabilities.

This research addresses a fundamental computational bottleneck in machine learning optimization workflows. Decision-focused learning, which trains predictive models directly for downstream optimization tasks rather than pure accuracy, has gained traction in operations research and finance. However, the requirement to solve constrained optimization problems repeatedly during training makes it prohibitively expensive for large-scale applications. The proposed Lagrangian decomposition framework breaks this computational barrier by enabling efficient problem decomposition, allowing parallel processing of subproblems that would otherwise require sequential solving.

The significance lies in bridging the gap between theoretical promise and practical deployment of decision-focused methods. Previous work remained limited to smaller problem instances due to computational constraints. By demonstrating scalability improvements—handling problems with eight times more variables—the framework opens applications in portfolio optimization, resource allocation, and supply chain management where problem sizes have historically exceeded practical limits.

For practitioners in optimization-heavy domains, this represents a meaningful advancement in making machine learning pipelines more efficient without sacrificing solution quality. The seamless integration with existing decision-focused methods like SPO+ and IMLE means adoption doesn't require architectural overhauls. The availability of open-source implementation reduces barriers to adoption.

Future developments will likely focus on applying this decomposition strategy to other constrained learning paradigms and exploring hybrid approaches that further balance computational efficiency with solution optimality. The framework's parallelization characteristics align well with modern distributed computing infrastructure, potentially enabling enterprise-scale deployments of decision-focused learning systems.

• →Lagrangian decomposition framework reduces computational costs of decision-focused learning while maintaining competitive performance on optimization problems.
• →Demonstrated scalability improvements handle problems with 8x more variables than previous related work.
• →Framework integrates seamlessly with existing decision-focused methods including SPO+ and IMLE without requiring architectural changes.
• →Parallelization capability enables efficient distributed processing of decomposed subproblems.
• →Open-source implementation available, reducing adoption barriers for researchers and practitioners.