Managing Solution Stability in Decision-Focused Learning with Cost Regularization

Victor Spitzer; Francois Sanson

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arXiv · 2601.21883

Managing Solution Stability in Decision-Focused Learning with Cost Regularization

Victor Spitzer·Francois Sanson

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Abstract

Decision-focused learning integrates predictive modeling and combinatorial optimization by training models to directly improve decision quality rather than prediction accuracy alone. Differentiating through combinatorial optimization problems represents a central challenge, and recent approaches tackle this difficulty by introducing perturbation-based approximations. In this work, we focus on estimating the objective function coefficients of a combinatorial optimization problem. Our study demonstrates that fluctuations in perturbation intensity occurring during the learning phase can lead to ineffective training, by establishing a theoretical link to the notion of solution stability in combinatorial optimization. We propose addressing this issue by introducing a regularization of the estimated cost vectors which improves the robustness and reliability of the learning process, as demonstrated by extensive numerical experiments.

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Victor Spitzer, Francois Sanson. 2026-01-29. Managing Solution Stability in Decision-Focused Learning with Cost Regularization. https://arxiv.org/abs/2601.21883

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