Solver-Free Decision-Focused Learning for Linear Optimization Problems

• URL: http://arxiv.org/abs/2505.22224v1
• Date: Wed, 28 May 2025 10:55:16 GMT
• Title: Solver-Free Decision-Focused Learning for Linear Optimization Problems
• Authors: Senne Berden, Ali İrfan Mahmutoğulları, Dimos Tsouros, Tias Guns,
• Abstract summary: In many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features.<n>This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization.<n>We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality.
• Score: 6.305123652677644
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features. This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization. A growing body of work on decision-focused learning (DFL) addresses this setting by training models specifically to produce predictions that maximize downstream decision quality, rather than accuracy. While effective, DFL is computationally expensive, because it requires solving the optimization problem with the predicted parameters at each loss evaluation. In this work, we address this computational bottleneck for linear optimization problems, a common class of problems in both DFL literature and real-world applications. We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality. Our method is based on the insight that a solution is optimal if and only if it achieves an objective value that is at least as good as that of its adjacent vertices on the feasible polytope. Building on this, our method compares the estimated quality of the ground-truth optimal solution with that of its precomputed adjacent vertices, and uses this as loss function. Experiments demonstrate that our method significantly reduces computational cost while maintaining high decision quality.

Related papers

• Online Decision-Focused Learning [63.83903681295497]
  Decision-focused learning (DFL) is an increasingly popular paradigm for training predictive models whose outputs are used in decision-making tasks.<n>We investigate DFL in dynamic environments where the objective function does not evolve over time.<n>We establish bounds on the expected dynamic regret, both when decision space is a simplex and when it is a general bounded convex polytope.
  arXiv  Detail & Related papers  (2025-05-19T10:40:30Z)
• 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)
• End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty [55.04219793298687]
  The Predict-Then-Forecast (PtO) paradigm in machine learning aims to maximize downstream decision quality. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives. It shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.
  arXiv  Detail & Related papers  (2024-02-12T16:33:35Z)
• 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)
• Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming [10.06803520598035]
  We develop a new approach to the problem called maximum optimality margin which the machine learning loss function by the optimality condition of the downstream optimization.
  arXiv  Detail & Related papers  (2023-01-26T17:53:38Z)
• Teaching Networks to Solve Optimization Problems [13.803078209630444]
  We propose to replace the iterative solvers altogether with a trainable parametric set function. We show the feasibility of learning such parametric (set) functions to solve various classic optimization problems.
  arXiv  Detail & Related papers  (2022-02-08T19:13:13Z)
• 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)
• Self-Directed Online Machine Learning for Topology Optimization [58.920693413667216]
  Self-directed Online Learning Optimization integrates Deep Neural Network (DNN) with Finite Element Method (FEM) calculations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 5 orders of magnitude compared with directly using methods, and outperformed all state-of-the-art algorithms tested in our experiments.
  arXiv  Detail & Related papers  (2020-02-04T20:00:28Z)

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.