Towards Robust Learning to Optimize with Theoretical Guarantees

Qingyu Song, Wei Lin, Juncheng Wang, Hong Xu

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

Abstract

Learning to optimize (L2O) is an emerging technique to solve mathematical optimization problems with learning-based methods. Although with great success in many real-world scenarios such as wireless communications computer networks and electronic design existing L2O works lack theoretical demonstration of their performance and robustness in out-of-distribution (OOD) scenarios. We address this gap by providing comprehensive proofs. First we prove a sufficient condition for a robust L2O model with homogeneous convergence rates over all In-Distribution (InD) instances. We assume an L2O model achieves robustness for an InD scenario. Based on our proposed methodology of aligning OOD problems to InD problems we also demonstrate that the L2O model's convergence rate in OOD scenarios will deteriorate by an equation of the L2O model's input features. Moreover we propose an L2O model with a concise gradient-only feature construction and a novel gradient-based history modeling method. Numerical simulation demonstrates that our proposed model outperforms the state-of-the-art baseline in both InD and OOD scenarios and achieves up to 10 x convergence speedup. The code of our method can be found from https://github.com/NetX-lab/GoMathL2O-Official.
Original languageEnglish
Title of host publicationProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024
Pages27498-27506
Number of pages9
Publication statusPublished - 21 Jun 2024
Event37th IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024 - Seattle Convention Center, Seattle, United States
Duration: 17 Jun 202421 Jun 2024
https://cvpr.thecvf.com/Conferences/2024 (Link to conference website)

Conference

Conference37th IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024
Country/TerritoryUnited States
CitySeattle
Period17/06/2421/06/24
Internet address

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