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Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…

Optimization and Control · Mathematics 2024-12-25 Quan Xiao , Tianyi Chen

Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…

Optimization and Control · Mathematics 2026-04-29 Lesi Chen , Jing Xu , Jingzhao Zhang

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

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

Recently, bi-level optimization (BLO) has taken center stage in some very exciting developments in the area of signal processing (SP) and machine learning (ML). Roughly speaking, BLO is a classical optimization problem that involves two…

Machine Learning · Computer Science 2023-12-22 Yihua Zhang , Prashant Khanduri , Ioannis Tsaknakis , Yuguang Yao , Mingyi Hong , Sijia Liu

Bilevel optimization (BLO) is a popular approach with many applications including hyperparameter optimization, neural architecture search, adversarial robustness and model-agnostic meta-learning. However, the approach suffers from time and…

Machine Learning · Computer Science 2021-06-08 Valerii Likhosherstov , Xingyou Song , Krzysztof Choromanski , Jared Davis , Adrian Weller

A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…

Optimization and Control · Mathematics 2018-12-05 Gernot Holler , Karl Kunisch , Richard C. Barnard

We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome…

Optimization and Control · Mathematics 2019-07-11 Johanna Burtscheidt , Matthias Claus

Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…

Machine Learning · Statistics 2023-08-03 Meng Qi , Paul Grigas , Zuo-Jun Max Shen

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Optimization and Control · Mathematics 2025-04-08 Prashant Khanduri , Ioannis Tsaknakis , Yihua Zhang , Sijia Liu , Mingyi Hong

In this paper, we propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by…

Optimization and Control · Mathematics 2023-02-08 Xiaoxiao Ma , Wei Yao , Jane J. Ye , Jin Zhang

This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by…

Optimization and Control · Mathematics 2019-11-06 Patrick Mehlitz , Alain B. Zemkoho

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

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

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

The bilevel program is an optimization problem where the constraint involves solutions to a parametric optimization problem. It is well-known that the value function reformulation provides an equivalent single-level optimization problem but…

Optimization and Control · Mathematics 2020-11-19 Kuang Bai , Jane Ye

Bilevel optimization is a popular two-level hierarchical optimization, which has been widely applied to many machine learning tasks such as hyperparameter learning, meta learning and continual learning. Although many bilevel optimization…

Optimization and Control · Mathematics 2023-11-21 Feihu Huang

Stochastic bilevel optimization generalizes the classic stochastic optimization from the minimization of a single objective to the minimization of an objective function that depends the solution of another optimization problem. Recently,…

Optimization and Control · Mathematics 2022-04-01 Tianyi Chen , Yuejiao Sun , Quan Xiao , Wotao Yin

(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

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