Scalable Decision Focused Learning via Online Trainable Surrogates

SCALABLE DECISION FOCUSED LEARNING VIA ON- LINE TRAINABLE SURROGATES Gaetano Signorelli and Michele Lombardi University of Bologna {gaetano.signorelli2, michele.lombardi2}@unibo.it ABSTRACT Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to suboptimal solutions. Using the actual decision cost as a loss function (called Decision Focused Learning) can address this issue, but with a severe loss of scalability at training time. To address this issue, we propose an acceleration method based on replacing costly loss function evaluations with an efficient surrogate. Unlike previously defined surrogates, our ap- proach relies on unbiased estimators – reducing the risk of spurious local optima – and can provide information on its local confidence – allowing one to switch to a fallback method when needed. Furthermore, the surrogate is designed for a black-box setting, which enables compensating for simplifications in the optimization model and account- ing for recourse actions during cost computation. In our results, the method reduces costly inner solver calls, with a solution quality comparable to other state-of-the-art techniques. 1 INTRODUCTION Many real-world decision support systems, in domains such as logistics or production planning, rely on the solution of constrained optimization problems with parameters that are estimated via Machine Learning (ML) predictors. Literature from the last decade has showed how this approach, sometimes referred to as Prediction Focused Learning (PFL), can lead to poor decision quality due to a misalignment between the training objective (usually likelihood maximization) and the actual decision cost. Decision Focused Learning (DFL) (Amos & Kolter, 2017; Elmachtoub & Grigas, 2022) was then introduced to correct for this issue by training predictors for minimal decision regret. While remarkable progress in the field has been made (Mandi et al., 2024), we argue that, based on our experience with industrial optimization use cases, three issues still prevent DFL from finding widespread practical application. First, while DFL methods are very efficient at inference time, their training scalability is often severely limited, since the problems encountered in decision support are frequently difficult (NP-hard or worse) and most DFL approaches require frequent solver calls and cost evaluations. Second, many DFL methods make restrictive assumptions on the decision problem (e.g. linear cost function, no parameters in the constraints); in addition to limiting applicability, it has been shown (Hu et al., 2022; Elmachtoub et al., 2023) that such assumptions also cause the DFL advantage to vanish if the parameters expectations can be accurately estimated (section A). Third, several DFL methods require explicit knowledge of the problem structure or the solver state, which in a practical setting would require costly refactoring of the existing tools, or even a radical change of the solution technology. Solving these issues would allow one to use DFL for improving the effectiveness and robustness of any real-world decision support tool, while maintaining scalability. We aim at making a significant step toward addressing these limitations, by relying on a carefully designed, efficient, surrogate to replace most solver calls at training time. Our surrogate is suitable 1 arXiv:2512.03861v1 [cs.LG] 3 Dec 2025 for a black-box setting, where no restrictive assumption is made on regret computation and no access to the solver state is needed. Compared to the relevant state of the art: 1) our surrogate is an asymptotically unbiased regret estimator, i.e. with no irreducible approximation error; 2) we use a principled mechanism (stochastic smoothing and importance sampling) to address 0-gradients often occurring in DFL settings; 3) we include uncertainty quantification via a confidence level, used to decide when to dynamically update the surrogate based on samples generated by a fallback method. Only a few of the existing DFL methods can be applied to achieve similar goals, a representative set of which is used as a baseline in our empirical evaluation. We design our experiments to assess the scalability and effectiveness of our method in a controlled setting, by comparing DFL and PFL on extended versions of standard benchmarks in the current literature. We emphasize problems with recourse actions and/or non-linearities, since they represent the settings where the benefits of DFL over PFL are robust even when accurate predictions can be obtained. We allow for scaling the problem complexity, to assess how the evaluated approaches behave on problems of different size (in terms of number of variables or parameters). In our results, our surrogate significantly reduces both the training runtime and the number of solver calls and c

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