Managing Solution Stability in Decision-Focused Learning with Cost Regularization

• URL: http://arxiv.org/abs/2601.21883v1
• Date: Thu, 29 Jan 2026 15:46:47 GMT
• Title: Managing Solution Stability in Decision-Focused Learning with Cost Regularization
• Authors: Victor Spitzer, Francois Sanson,
• Abstract summary: Decision-focused learning integrates predictive modeling and optimization by training models to directly improve decision quality.<n>Differentiating through optimization problems represents a central challenge, and recent approaches tackle this difficulty by introducing perturbation-based approximations.<n>Our study demonstrates that fluctuations in perturbation intensity occurring during the learning phase can lead to ineffective training.<n>We propose addressing this issue by introducing a regularization of the estimated cost which improves the robustness and reliability of the learning process.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Adaptive Learning-based Surrogate Method for Stochastic Programs with Implicitly Decision-dependent Uncertainty [1.5412450351033007]
  We consider a class of programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error.<n>We develop an adaptive learning-based surrogate method that integrates the simulation scheme and statistical estimates to construct estimation-based surrogate functions.
  arXiv  Detail & Related papers  (2025-05-12T07:35:06Z)
• Self-Supervised Penalty-Based Learning for Robust Constrained Optimization [4.297070083645049]
  We propose a new methodology for parameterized constrained robust optimization, based on learning with a self-supervised penalty-based loss function.<n>Our approach is able to effectively learn neural network approximations whose inference time is significantly smaller than the time of traditional solvers.
  arXiv  Detail & Related papers  (2025-03-07T06:42:17Z)
• Learning Joint Models of Prediction and Optimization [56.04498536842065]
  Predict-Then-Then framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models.
  arXiv  Detail & Related papers  (2024-09-07T19:52:14Z)
• Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling [0.0]
  This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA) Numerical experiments demonstrate that our method is a competitive general-purpose solver, achieving performance comparable to iSCO and learning-based solvers.
  arXiv  Detail & Related papers  (2024-09-02T12:55:27Z)
• Predict-Then-Optimize by Proxy: Learning Joint Models of Prediction and Optimization [59.386153202037086]
  Predict-Then- framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. This approach can be inefficient and requires handcrafted, problem-specific rules for backpropagation through the optimization step. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by predictive models.
  arXiv  Detail & Related papers  (2023-11-22T01:32:06Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Learning to Optimize with Stochastic Dominance Constraints [103.26714928625582]
  In this paper, we develop a simple yet efficient approach for the problem of comparing uncertain quantities. We recast inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.
  arXiv  Detail & Related papers  (2022-11-14T21:54:31Z)
• Careful! Training Relevance is Real [0.7742297876120561]
  We propose constraints designed to enforce training relevance. We show through a collection of experimental results that adding the suggested constraints significantly improves the quality of solutions.
  arXiv  Detail & Related papers  (2022-01-12T11:54:31Z)
• The Statistical Complexity of Interactive Decision Making [126.04974881555094]
  We provide a complexity measure, the Decision-Estimation Coefficient, that is proven to be both necessary and sufficient for sample-efficient interactive learning. A unified algorithm design principle, Estimation-to-Decisions (E2D), transforms any algorithm for supervised estimation into an online algorithm for decision making.
  arXiv  Detail & Related papers  (2021-12-27T02:53:44Z)
• USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems [9.015720257837575]
  We consider the regression between spaces, aiming to infer high-quality optimization solutions from samples of input-solution pairs. For learning foundations, we present learning-error analysis under the PAC-Bayesian framework. We obtain highly encouraging experimental results for several classic problems on both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-07-15T17:59:08Z)
• Automatically Learning Compact Quality-aware Surrogates for Optimization Problems [55.94450542785096]
  Solving optimization problems with unknown parameters requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in a complex training model pipeline results in predictions of iteration of unobserved decision making. We show that we can improve solution quality by learning a low-dimensional surrogate model of a large optimization problem.
  arXiv  Detail & Related papers  (2020-06-18T19:11:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.