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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

Bilevel programming has recently received attention in the literature due to its wide range of applications, including reinforcement learning and hyper-parameter optimization. However, it is widely assumed that the underlying bilevel…

Machine Learning · Computer Science 2024-10-11 Parvin Nazari , Ahmad Mousavi , Davoud Ataee Tarzanagh , George Michailidis

Bilevel optimization, in which one optimization problem is nested inside another, underlies many machine learning applications with a hierarchical structure -- such as meta-learning and hyperparameter optimization. Such applications often…

Machine Learning · Computer Science 2025-11-10 Andrew Lowy , Daogao 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 general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

Machine Learning · Statistics 2020-07-13 Riccardo Grazzi , Luca Franceschi , Massimiliano Pontil , Saverio Salzo

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…

Neural and Evolutionary Computing · Computer Science 2024-07-08 Ankur Sinha , Dhaval Pujara , Hemant Kumar Singh

We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…

Optimization and Control · Mathematics 2024-05-08 Ensio Suonperä , Tuomo Valkonen

Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…

Optimization and Control · Mathematics 2026-02-20 Henri Lefebvre , Martin Schmidt , Simon Stevens , Johannes Thürauf

Diffusion models, which iteratively denoise data samples to synthesize high-quality outputs, have achieved empirical success across domains. However, optimizing these models for downstream tasks often involves nested bilevel structures,…

Machine Learning · Computer Science 2025-08-06 Quan Xiao , Hui Yuan , A F M Saif , Gaowen Liu , Ramana Kompella , Mengdi Wang , Tianyi Chen

Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…

Optimization and Control · Mathematics 2022-06-14 Xuxing Chen , Minhui Huang , Shiqian Ma

Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces…

Machine Learning · Computer Science 2023-12-22 Yilang Zhang , Bingcong Li , Shijian Gao , Georgios B. Giannakis

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

In this work, we consider the bilevel optimization problem on Riemannian manifolds. We inspect the calculation of the hypergradient of such problems on general manifolds and thus enable the utilization of gradient-based algorithms to solve…

Optimization and Control · Mathematics 2024-02-09 Jiaxiang Li , Shiqian Ma

Motivated by emerging applications in wireless sensor networks and large-scale data processing, we consider distributed optimization over directed networks where the agents communicate their information locally to their neighbors to…

Optimization and Control · Mathematics 2021-03-22 Farzad Yousefian

In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in…

Optimization and Control · Mathematics 2026-01-22 Sudkobfa Boontawee , Mootta Prangprakhon , Nimit Nimana

In this work we derive a second-order approach to bilevel optimization, a type of mathematical programming in which the solution to a parameterized optimization problem (the "lower" problem) is itself to be optimized (in the "upper"…

Optimization and Control · Mathematics 2022-05-06 Robert Dyro , Edward Schmerling , Nikos Arechiga , Marco Pavone

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

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

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 programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…

Optimization and Control · Mathematics 2024-07-25 Bo Zhou , Ruiwei Jiang , Siqian Shen