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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

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

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

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

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

Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta-learning, continual learning, and reinforcement learning. Conventional BO…

Machine Learning · Computer Science 2022-09-20 Mao Ye , Bo Liu , Stephen Wright , Peter Stone , Qiang Liu

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…

Optimization and Control · Mathematics 2025-05-06 Youran Dong , Junfeng Yang , Wei Yao , Jin Zhang

Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient…

Optimization and Control · Mathematics 2026-02-04 Qichao Cao , Shangzhi Zeng , Jin Zhang

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

Optimization and Control · Mathematics 2023-04-25 Ruichen Jiang , Nazanin Abolfazli , Aryan Mokhtari , Erfan Yazdandoost Hamedani

This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…

Machine Learning · Computer Science 2025-01-16 Xiaochuan Gong , Jie Hao , Mingrui Liu

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…

Machine Learning · Computer Science 2025-01-08 Han Shen , Quan Xiao , Tianyi Chen

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Optimization and Control · Mathematics 2025-11-11 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

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

Bilevel optimization plays an essential role in many machine learning tasks, ranging from hyperparameter optimization to meta-learning. Existing studies on bilevel optimization, however, focus on either centralized or synchronous…

Machine Learning · Computer Science 2023-02-27 Yang Jiao , Kai Yang , Tiancheng Wu , Dongjin Song , Chengtao Jian

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

Optimization and Control · Mathematics 2024-06-03 Jincheng Cao , Ruichen Jiang , Erfan Yazdandoost Hamedani , Aryan Mokhtari

Approximate bi-level optimization (ABLO) consists of (outer-level) optimization problems, involving numerical (inner-level) optimization loops. While ABLO has many applications across deep learning, it suffers from time and memory…

Machine Learning · Computer Science 2021-06-09 Valerii Likhosherstov , Xingyou Song , Krzysztof Choromanski , Jared Davis , Adrian Weller

(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

Multi-Objective Bi-Level Optimization (MOBLO) addresses nested multi-objective optimization problems common in a range of applications. However, its multi-objective and hierarchical bilevel nature makes it notably complex. Gradient-based…

Optimization and Control · Mathematics 2024-06-11 Xinmin Yang , Wei Yao , Haian Yin , Shangzhi Zeng , Jin Zhang

Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple…

Optimization and Control · Mathematics 2023-10-09 Quan Xiao , Songtao Lu , Tianyi Chen

Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential…

Machine Learning · Computer Science 2023-03-01 Francesco Alesiani