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Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…

Machine Learning · Computer Science 2021-08-03 Kaiyi Ji

Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively…

Optimization and Control · Mathematics 2025-04-22 Guy Kornowski , Swati Padmanabhan , Kai Wang , Zhe Zhang , Suvrit Sra

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

While stochastic bilevel optimization methods have been extensively studied for addressing large-scale nested optimization problems in machine learning, it remains an open question whether the optimal complexity bounds for solving bilevel…

Optimization and Control · Mathematics 2026-03-24 Tianshu Chu , Dachuan Xu , Wei Yao , Jin Zhang

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 problems, encountered in fields such as economics, engineering, and machine learning, pose significant computational challenges due to their hierarchical structure and constraints at both upper and lower levels.…

Optimization and Control · Mathematics 2024-08-21 Mengwei Xu , Yu-Hong Dai , Xin-Wei Liu , Bo Wang

Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…

Optimization and Control · Mathematics 2025-05-19 Xiaotian Jiang , Ioannis Tsaknakis , Prashant Khanduri , Mingyi Hong

Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…

Optimization and Control · Mathematics 2023-07-24 Xiang Liu , Mengwei Xu , Liwei Zhang

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

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

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

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

We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with…

Optimization and Control · Mathematics 2026-02-06 Wei Shen , Jiawei Zhang , Minhui Huang , Cong Shen

Generalizing from a single labeled source domain to unseen target domains, without access to any target data during training, remains a fundamental challenge in robust machine learning. We address this underexplored setting, known as Single…

Machine Learning · Computer Science 2026-04-09 Marzi Heidari , Hanping Zhang , Hao Yan , Yuhong Guo

Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…

Optimization and Control · Mathematics 2026-05-28 Eduardo Nolasco , Ross D. King , Vassilios S. Vassiliadis

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

Bi-level optimization problems, where one wishes to find the global minimizer of an upper-level objective function over the globally optimal solution set of a lower-level objective, arise in a variety of scenarios throughout science and…

Optimization and Control · Mathematics 2025-05-13 Nicolás García Trillos , Sixu Li , Konstantin Riedl , Yuhua Zhu

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 formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…

Machine Learning · Computer Science 2024-01-19 Jie Hao , Xiaochuan Gong , Mingrui Liu

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…

Machine Learning · Statistics 2018-07-04 Luca Franceschi , Paolo Frasconi , Saverio Salzo , Riccardo Grazzi , Massimilano Pontil