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Learning to Optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine learning to enhance conventional optimization techniques. As real-world optimization problems…

Optimization and Control · Mathematics 2024-05-27 Xiaohan Chen , Jialin Liu , Wotao Yin

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…

Machine Learning · Computer Science 2025-06-18 Qingyu Song , Wei Lin , Juncheng Wang , Hong Xu

Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering. It automates the design of an optimization method based on…

Optimization and Control · Mathematics 2021-07-05 Tianlong Chen , Xiaohan Chen , Wuyang Chen , Howard Heaton , Jialin Liu , Zhangyang Wang , Wotao Yin

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…

Optimization and Control · Mathematics 2025-12-04 James Kotary , Himanshu Sharma , Ethan King , Draguna Vrabie , Ferdinando Fioretto , Jan Drgona

While large language models (LLMs) have shown strong performance in math and logic reasoning, their ability to handle combinatorial optimization (CO) -- searching high-dimensional solution spaces under hard constraints -- remains…

Artificial Intelligence · Computer Science 2026-04-13 Xia Jiang , Jing Chen , Cong Zhang , Jie Gao , Chengpeng Hu , Chenhao Zhang , Yaoxin Wu , Yingqian Zhang

Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…

Optimization and Control · Mathematics 2024-09-27 Ling Liang , Cameron Austin , Haizhao Yang

Learning to Optimize (L2O) enhances optimization efficiency with integrated neural networks. L2O paradigms achieve great outcomes, e.g., refitting optimizer, generating unseen solutions iteratively or directly. However, conventional L2O…

Machine Learning · Computer Science 2025-03-17 Mingjia Shi , Ruihan Lin , Xuxi Chen , Yuhao Zhou , Zezhen Ding , Pingzhi Li , Tong Wang , Kai Wang , Zhangyang Wang , Jiheng Zhang , Tianlong Chen

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm…

Machine Learning · Computer Science 2025-10-31 Fu Luo , Xi Lin , Mengyuan Zhong , Fei Liu , Zhenkun Wang , Jianyong Sun , Qingfu Zhang

Neural combinatorial optimization (NCO) aims at designing problem-independent and efficient neural network-based strategies for solving combinatorial problems. The field recently experienced growth by successfully adapting architectures…

Machine Learning · Computer Science 2020-11-13 Michal Lisicki , Arash Afkanpour , Graham W. Taylor

Combinatorial optimization (CO) is fundamental to several real-world applications, from logistics and scheduling to hardware design and resource allocation. Deep reinforcement learning (RL) has recently shown significant benefits in solving…

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…

Machine Learning · Computer Science 2021-10-26 Runzhong Wang , Zhigang Hua , Gan Liu , Jiayi Zhang , Junchi Yan , Feng Qi , Shuang Yang , Jun Zhou , Xiaokang Yang

This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in…

Machine Learning · Computer Science 2020-06-23 Ruben Solozabal , Josu Ceberio , Martin Takáč

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…

Machine Learning · Computer Science 2025-11-24 Yuanyao Chen , Rongsheng Chen , Fu Luo , Zhenkun Wang

Learning to optimize (L2O) has gained increasing attention since classical optimizers require laborious problem-specific design and hyperparameter tuning. However, there is a gap between the practical demand and the achievable performance…

Machine Learning · Computer Science 2020-10-20 Tianlong Chen , Weiyi Zhang , Jingyang Zhou , Shiyu Chang , Sijia Liu , Lisa Amini , Zhangyang Wang

Learning to Optimize (LtO) is a problem setting in which a machine learning (ML) model is trained to emulate a constrained optimization solver. Learning to produce optimal and feasible solutions subject to complex constraints is a difficult…

Machine Learning · Computer Science 2024-03-18 James Kotary , Ferdinando Fioretto

Learn to Optimize (L2O) trains deep neural network-based solvers for optimization, achieving success in accelerating convex problems and improving non-convex solutions. However, L2O lacks rigorous theoretical backing for its own training…

Machine Learning · Computer Science 2025-12-24 Qingyu Song , Wei Lin , Hong Xu

Recent studies on Learning to Optimize (L2O) suggest a promising path to automating and accelerating the optimization procedure for complicated tasks. Existing L2O models parameterize optimization rules by neural networks, and learn those…

Machine Learning · Computer Science 2022-05-10 Wenqing Zheng , Tianlong Chen , Ting-Kuei Hu , Zhangyang Wang

Neural combinatorial optimization (NCO) is a promising learning-based approach for solving challenging combinatorial optimization problems without specialized algorithm design by experts. However, most constructive NCO methods cannot solve…

Machine Learning · Computer Science 2024-01-17 Fu Luo , Xi Lin , Fei Liu , Qingfu Zhang , Zhenkun Wang

The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes.…

Systems and Control · Electrical Eng. & Systems 2024-06-04 Andrea Martin , Luca Furieri
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