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We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…

Optimization and Control · Mathematics 2025-09-29 Khanh-Hung Giang-Tran , Nam Ho-Nguyen , Fatma Kılınç-Karzan , Lingqing Shen

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…

Optimization and Control · Mathematics 2026-05-11 Yiyang Shen , Yutian He , Weiran Wang , Qihang Lin

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…

Machine Learning · Computer Science 2023-03-16 Meng Ding , Mingxi Lei , Yunwen Lei , Di Wang , Jinhui Xu

This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…

Machine Learning · Computer Science 2023-05-26 Nicolas Zucchet , João Sacramento

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the…

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

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

Optimization and Control · Mathematics 2026-02-06 Mattia Solla , Johannes O. Royset

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

Optimization and Control · Mathematics 2024-11-05 Andi Han , Bamdev Mishra , Pratik Jawanpuria , Akiko Takeda

Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms and has been applied to many machine learning tasks such as data cleaning, few-shot learning, and neural architecture search. However,…

Machine Learning · Computer Science 2022-05-04 Junyi Li , Feihu Huang , Heng Huang

Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…

Optimization and Control · Mathematics 2024-11-12 Junyi Li , Heng Huang

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…

Machine Learning · Computer Science 2021-12-17 Junjie Yang , Kaiyi Ji , Yingbin Liang

In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $\epsilon$-stationary point within…

Optimization and Control · Mathematics 2026-05-26 Lesi Chen , Yaohua Ma , Jingzhao Zhang

In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming…

Optimization and Control · Mathematics 2025-04-17 Stephan Dempe , Joydeep Duta , Tanushree Pandit , K. S. Mallikarjuna Rao

Bilevel optimization has arisen as a powerful tool for solving a variety of machine learning problems. Two current popular bilevel optimizers AID-BiO and ITD-BiO naturally involve solving one or two sub-problems, and consequently, whether…

Machine Learning · Computer Science 2022-06-02 Kaiyi Ji , Mingrui Liu , Yingbin Liang , Lei Ying

Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…

Machine Learning · Computer Science 2024-11-05 Xiaoyu Wang , Rui Pan , Renjie Pi , Jipeng Zhang

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Machine Learning · Statistics 2024-12-10 Ieva Petrulionyte , Julien Mairal , Michael Arbel

This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes…

Computer Vision and Pattern Recognition · Computer Science 2021-12-30 Risheng Liu , Long Ma , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

Bilevel optimization has found extensive applications in modern machine learning problems such as hyperparameter optimization, neural architecture search, meta-learning, etc. While bilevel problems with a unique inner minimal point (e.g.,…

Optimization and Control · Mathematics 2022-06-09 Daouda Sow , Kaiyi Ji , Ziwei Guan , Yingbin Liang

Bilevel optimization has become a powerful tool in a wide variety of machine learning problems. However, the current nonconvex bilevel optimization considers an offline dataset and static functions, which may not work well in emerging…

Optimization and Control · Mathematics 2023-11-10 Sen Lin , Daouda Sow , Kaiyi Ji , Yingbin Liang , Ness Shroff

Bilevel optimization problems involve two nested objectives, where an upper-level objective depends on a solution to a lower-level problem. When the latter is non-convex, multiple critical points may be present, leading to an ambiguous…

Optimization and Control · Mathematics 2022-10-18 Michael Arbel , Julien Mairal

Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex…

Machine Learning · Computer Science 2025-11-27 Kaiyi Ji