English
Related papers

Related papers: Towards Gradient-based Bilevel Optimization with N…

200 papers

Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks,…

Machine Learning · Computer Science 2021-09-29 Risheng Liu , Jiaxin Gao , Jin Zhang , Deyu Meng , Zhouchen Lin

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems,…

Machine Learning · Computer Science 2022-12-29 Paul Vicol , Jonathan Lorraine , Fabian Pedregosa , David Duvenaud , Roger Grosse

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

Optimization and Control · Mathematics 2024-03-15 Nazanin Abolfazli , Ruichen Jiang , Aryan Mokhtari , Erfan Yazdandoost Hamedani

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level…

Machine Learning · Computer Science 2026-05-15 Zhiyao Zhang , Myeung Suk Oh , Zhen Qin , Jiaxiang Li , Xin Zhang , Jia Liu

Two-level stochastic optimization formulations have become instrumental in a number of machine learning contexts such as continual learning, neural architecture search, adversarial learning, and hyperparameter tuning. Practical stochastic…

Optimization and Control · Mathematics 2023-11-08 Tommaso Giovannelli , Griffin Dean Kent , Luis Nunes Vicente

Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based…

Optimization and Control · Mathematics 2024-08-27 Liuyuan Jiang , Quan Xiao , Victor M. Tenorio , Fernando Real-Rojas , Antonio G. Marques , Tianyi Chen

Recent optimizers such as Lion and Muon have demonstrated strong empirical performance by normalizing gradient momentum via linear minimization oracles (LMOs). While variance reduction has been explored to accelerate LMO-based methods, it…

Machine Learning · Computer Science 2026-05-08 Won-Jun Jang , Si-Hyeon Lee

This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These…

Optimization and Control · Mathematics 2024-05-17 Risheng Liu , Zhu Liu , Wei Yao , Shangzhi Zeng , Jin Zhang

In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…

Machine Learning · Computer Science 2022-06-28 Jingyuan Xia , Shengxi Li , Jun-Jie Huang , Imad Jaimoukha , Deniz Gunduz

We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…

Optimization and Control · Mathematics 2026-05-06 Yara Elshiaty , Stefania Petra

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

Machine Learning · Computer Science 2024-10-16 Yuntian Gu , Xuzheng Chen

In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through…

Machine Learning · Computer Science 2017-07-11 Li Chen , Shuisheng Zhou , Zhuan Zhang

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

Optimization and Control · Mathematics 2026-02-23 Matthew X. Burns , Jiaming Liang

Trilevel learning, also called trilevel optimization (TLO), has been recognized as a powerful modelling tool for hierarchical decision process and widely applied in many machine learning applications, such as robust neural architecture…

Machine Learning · Computer Science 2024-01-23 Yang Jiao , Kai Yang , Tiancheng Wu , Chengtao Jian , Jianwei Huang

Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…

Optimization and Control · Mathematics 2024-06-05 Wei Yao , Haian Yin , Shangzhi Zeng , Jin Zhang

Penalty-based methods have become popular for solving bilevel optimization (BLO) problems, thanks to their effective first-order nature. However, they often require inner-loop iterations to solve the lower-level (LL) problem and small…

Optimization and Control · Mathematics 2025-11-24 Liuyuan Jiang , Quan Xiao , Lisha Chen , Tianyi Chen

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

Black-Box Optimization (BBO) methods can find optimal policies for systems that interact with complex environments with no analytical representation. As such, they are of interest in many Artificial Intelligence (AI) domains. Yet classical…

Machine Learning · Computer Science 2020-06-17 Mor Sinay , Elad Sarafian , Yoram Louzoun , Noa Agmon , Sarit Kraus

Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…

Machine Learning · Computer Science 2019-12-03 Fanhua Shang , Bingkun Wei , Hongying Liu , Yuanyuan Liu , Jiacheng Zhuo

A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…

Optimization and Control · Mathematics 2012-09-21 Quoc Tran Dinh , Ion Necoara , Moritz Diehl