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This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…

Optimization and Control · Mathematics 2025-11-06 Dhaval Pujara , Ankur Sinha

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Optimization and Control · Mathematics 2022-02-16 Meng Li , Paul Grigas , Alper Atamturk

Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…

Optimization and Control · Mathematics 2024-09-04 Wanli Shi , Yi Chang , Bin Gu

This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…

Optimization and Control · Mathematics 2026-02-05 Demyan Yarmoshik , Nhat Trung Nguyen , Alexander Rogozin , Alexander Gasnikov

In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and…

Optimization and Control · Mathematics 2026-05-15 Xiaotian Jiang , Chang He , Mingyi Hong , Shuzhong Zhang

In this paper, we study a class of bilevel optimization program (BP), where the feasible set of the lower level program is independent of the upper level variable. For bilevel programs it is known that the first order approach requires the…

Optimization and Control · Mathematics 2026-02-27 Kuang Bai , Wei Yao , Jane J. Ye , Jin Zhang

Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community including hyperparameter optimization and meta-knowledge extraction. Bi-level optimization embeds one problem within another…

Machine Learning · Computer Science 2023-07-11 Can Chen , Xi Chen , Chen Ma , Zixuan Liu , Xue Liu

Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…

Machine Learning · Computer Science 2023-03-28 Hongchang Gao , Bin Gu , My T. Thai

In this article, we investigate a time-optimal state-constrained bilevel optimal control problem whose lower-level dynamics feature a sweeping control process involving a {\it truncated normal cone}. By bilevel, it is meant that the…

Optimization and Control · Mathematics 2022-01-07 Nathalie T. Khalil , Fernando Lobo Pereira

Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function, appears in many areas of machine learning. In a large scale empirical risk minimization setting where the number of samples…

Machine Learning · Statistics 2024-12-03 Mathieu Dagréou , Pierre Ablin , Samuel Vaiter , Thomas Moreau

Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…

Machine Learning · Computer Science 2026-04-23 Xuelin Zhang , Peipei Yuan

Usually, bilevel optimization problems need to be transformed into single-level ones in order to derive optimality conditions and solution algorithms. Among the available approaches, the replacement of the lower-level problem by means of…

Optimization and Control · Mathematics 2025-02-17 Stephan Dempe , Patrick Mehlitz

This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…

Optimization and Control · Mathematics 2025-11-18 Cac Phan , Kai Wang

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

In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…

Machine Learning · Computer Science 2020-02-11 Ashwinkumar Badanidiyuru , Amin Karbasi , Ehsan Kazemi , Jan Vondrak

Self-concordant barriers are essential for interior-point algorithms in conic programming. To speed up the convergence it is of interest to find a barrier with the lowest possible parameter for a given cone. The barrier parameter is a…

Optimization and Control · Mathematics 2025-07-08 Vitali Pirau , Roland Hildebrand

Model predictive control (MPC) has been widely used in many fields, often in hierarchical architectures that combine controllers and decision-making layers at different levels. However, when such architectures are cast as bilevel…

Systems and Control · Electrical Eng. & Systems 2026-04-01 Ryuta Moriyasu , Carmen Amo Alonso , Marco Pavone

The literature on pessimistic linear bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In…

Optimization and Control · Mathematics 2026-05-08 Dorothee Henke , Henri Lefebvre , Martin Schmidt , Johannes Thürauf

In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…

Statistics Theory · Mathematics 2019-06-18 Kinjal Basu , Preetam Nandy

In this paper, we consider non-convex stochastic bilevel optimization (SBO) problems that have many applications in machine learning. Although numerous studies have proposed stochastic algorithms for solving these problems, they are limited…

Optimization and Control · Mathematics 2021-06-15 Zhishuai Guo , Quanqi Hu , Lijun Zhang , Tianbao Yang