CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs

• URL: http://arxiv.org/abs/2312.07718v2
• Date: Fri, 15 Mar 2024 21:45:39 GMT
• Title: CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs
• Authors: Bo Tang, Elias B. Khalil,
• Abstract summary: This work focuses on binary linear programs (BLPs) and proposes a new end-to-end training method to predict-then-optimize. Our method, Cone-aligned Vector Estimation (CaVE), aligns the predicted cost vectors with the normal cone corresponding to the true optimal solution of a training instance.
• Score: 23.00554768496448
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The end-to-end predict-then-optimize framework, also known as decision-focused learning, has gained popularity for its ability to integrate optimization into the training procedure of machine learning models that predict the unknown cost (objective function) coefficients of optimization problems from contextual instance information. Naturally, most of the problems of interest in this space can be cast as integer linear programs. In this work, we focus on binary linear programs (BLPs) and propose a new end-to-end training method to predict-then-optimize. Our method, Cone-aligned Vector Estimation (CaVE), aligns the predicted cost vectors with the normal cone corresponding to the true optimal solution of a training instance. When the predicted cost vector lies inside the cone, the optimal solution to the linear relaxation of the binary problem is optimal. This alignment not only produces decision-aware learning models but also dramatically reduces training time as it circumvents the need to solve BLPs to compute a loss function with its gradients. Experiments across multiple datasets show that our method exhibits a favorable trade-off between training time and solution quality, particularly with large-scale optimization problems such as vehicle routing, a hard BLP that has yet to benefit from predict-then-optimize methods in the literature due to its difficulty.

Related papers

• Learning Constrained Optimization with Deep Augmented Lagrangian Methods [54.22290715244502]
  A machine learning (ML) model is trained to emulate a constrained optimization solver. This paper proposes an alternative approach, in which the ML model is trained to predict dual solution estimates directly. It enables an end-to-end training scheme is which the dual objective is as a loss function, and solution estimates toward primal feasibility, emulating a Dual Ascent method.
  arXiv  Detail & Related papers  (2024-03-06T04:43:22Z)
• 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)
• Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization [12.610576072466895]
  We consider the inverse problem where we use prior decision data to uncover the underlying decision-making process. This statistical learning problem is referred to as data-driven inverse optimization. We propose an efficient block coordinate descent-based algorithm to solve large problem instances.
  arXiv  Detail & Related papers  (2022-10-27T12:52:56Z)
• 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)
• Divide and Learn: A Divide and Conquer Approach for Predict+Optimize [50.03608569227359]
  The predict+optimize problem combines machine learning ofproblem coefficients with a optimization prob-lem that uses the predicted coefficients. We show how to directlyexpress the loss of the optimization problem in terms of thepredicted coefficients as a piece-wise linear function. We propose a novel divide and algorithm to tackle optimization problems without this restriction and predict itscoefficients using the optimization loss.
  arXiv  Detail & Related papers  (2020-12-04T00:26:56Z)
• Contrastive Losses and Solution Caching for Predict-and-Optimize [19.31153168397003]
  We use a Noise Contrastive approach to motivate a family of surrogate loss functions. We address a major bottleneck of all predict-and-optimize approaches. We show that even a very slow growth rate is enough to match the quality of state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-11-10T19:09:12Z)
• Fast Rates for Contextual Linear Optimization [52.39202699484225]
  We show that a naive plug-in approach achieves regret convergence rates that are significantly faster than methods that directly optimize downstream decision performance. Our results are overall positive for practice: predictive models are easy and fast to train using existing tools, simple to interpret, and, as we show, lead to decisions that perform very well.
  arXiv  Detail & Related papers  (2020-11-05T18:43:59Z)
• Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization [12.610576072466895]
  This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. We introduce a new formulation of the problem that, compared to other existing methods, allows the recovery of a less restrictive and generally more appropriate admissible set of cost estimates.
  arXiv  Detail & Related papers  (2020-09-16T22:25:31Z)
• 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.