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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 learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

Optimization and Control · Mathematics 2025-05-20 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

This review discusses methods for learning parameters for image reconstruction problems using bilevel formulations. Image reconstruction typically involves optimizing a cost function to recover a vector of unknown variables that agrees with…

Optimization and Control · Mathematics 2022-06-16 Caroline Crockett , Jeffrey A. Fessler

In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…

Optimization and Control · Mathematics 2018-02-08 Saeed Ghadimi , Mengdi Wang

We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…

Optimization and Control · Mathematics 2023-11-20 Sepideh Samadi , Daniel Burbano , Farzad Yousefian

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

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

We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…

Optimization and Control · Mathematics 2025-04-14 Sepideh Samadi , Daniel Burbano , Farzad Yousefian

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 this paper, we present difference of convex algorithms for solving bilevel programs in which the upper level objective functions are difference of convex functions, and the lower level programs are fully convex. This nontrivial class of…

Optimization and Control · Mathematics 2022-08-30 Jane J. Ye , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Machine Learning · Computer Science 2023-08-22 Siyuan Xu , Minghui Zhu

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

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

In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…

Optimization and Control · Mathematics 2025-03-14 Xiaotian Jiang , Jiaxiang Li , Mingyi Hong , Shuzhong Zhang

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

Optimization and Control · Mathematics 2025-01-28 Huaqing Zhang , Lesi Chen , Jing Xu , Jingzhao Zhang

Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…

Optimization and Control · Mathematics 2026-03-03 Yuman Wu , Xiaochuan Gong , Jie Hao , Mingrui Liu

We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…

Optimization and Control · Mathematics 2016-04-27 Peter Ochs , René Ranftl , Thomas Brox , Thomas Pock

We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…

Optimization and Control · Mathematics 2018-09-27 Mostafa Amini , Farzad Yousefian

Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…

Optimization and Control · Mathematics 2023-02-21 Feihu Huang , Junyi Li , Shangqian Gao

Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…

Optimization and Control · Mathematics 2017-09-27 Aurélien Ouattara , Anil Aswani
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