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Related papers: CB$^2$O: Consensus-Based Bi-Level Optimization

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We introduce a new stochastic differential model for global optimization of nonconvex functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto-Vicsek system and belongs to the class of Consensus-Based…

Analysis of PDEs · Mathematics 2021-07-29 Massimo Fornasier , Hui Huang , Lorenzo Pareschi , Philippe Sünnen

This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes…

Computer Vision and Pattern Recognition · Computer Science 2021-12-30 Risheng Liu , Long Ma , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…

Optimization and Control · Mathematics 2021-10-14 Hyeong-Ohk Bae , Seung-Yeal Ha , Myeongju Kang , Hyuncheul Lim , Chanho Min , Jane Yoo

This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary…

Optimization and Control · Mathematics 2020-03-09 Joerg Fliege , Andrey Tin , Alain Zemkoho

Online bilevel optimization (OBO) is a powerful framework for machine learning problems where both outer and inner objectives evolve over time, requiring dynamic updates. Current OBO approaches rely on deterministic \textit{window-smoothed}…

Machine Learning · Computer Science 2026-05-20 Parvin Nazari , Bojian Hou , Davoud Ataee Tarzanagh , Li Shen , George Michailidis

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

In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…

Optimization and Control · Mathematics 2022-08-03 Giacomo Borghi , Michael Herty , Lorenzo Pareschi

Online bilevel optimization (OBO) has emerged as a powerful framework for many machine learning problems. Prior works have developed several algorithms that minimize the standard bilevel local regret or the window-averaged bilevel local…

Machine Learning · Computer Science 2026-05-12 Tingkai Jia , Haiguang Wang , Cheng Chen

Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}) parameters) to set step sizes, a…

Optimization and Control · Mathematics 2026-01-01 Xu Shi , Yinglin Du , Rufeng Xiao , Rujun Jiang

We introduce a novel first-order stochastic swarm intelligence (SI) model in the spirit of consensus formation models, namely a consensus-based optimization (CBO) algorithm, which may be used for the global optimization of a function in…

Probability · Mathematics 2017-10-06 René Pinnau , Claudia Totzeck , Oliver Tse , Stephan Martin

Bilevel optimization (BO) is widely applicable to many machine learning problems. Scaling BO, however, requires repeatedly computing hypergradients, which involves solving inverse Hessian-vector products (IHVPs). In practice, these…

Machine Learning · Computer Science 2026-04-01 Disen Liao , Felix Dangel , Yaoliang Yu

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…

Optimization and Control · Mathematics 2025-02-28 Yan Yang , Bin Gao , Ya-xiang Yuan

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 optimization has become a powerful tool in a wide variety of machine learning problems. However, the current nonconvex bilevel optimization considers an offline dataset and static functions, which may not work well in emerging…

Optimization and Control · Mathematics 2023-11-10 Sen Lin , Daouda Sow , Kaiyi Ji , Yingbin Liang , Ness Shroff

This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order…

Optimization and Control · Mathematics 2026-03-10 Lesi Chen , Junru Li , El Mahdi Chayti , Jingzhao Zhang

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

Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…

Optimization and Control · Mathematics 2020-05-19 Ron Estrin , Michael P. Friedlander

Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is…

Machine Learning · Computer Science 2022-03-29 Guangmo Tong

Introduced in 2017 \cite{B1-pinnau2017consensus}, Consensus-Based Optimization (CBO) has rapidly emerged as a significant breakthrough in global optimization. This straightforward yet powerful multi-particle, zero-order optimization method…

Analysis of PDEs · Mathematics 2025-05-29 Massimo Fornasier , Lukang Sun

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