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

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In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed…

Optimization and Control · Mathematics 2020-02-20 Changxin Liu , Huiping Li , Yang Shi

We consider bilevel optimization problems with general nonconvex lower-level objectives and show that the classical hyperfunction-based formulation is unsettled, since the global minimizer of the lower-level problem is generally…

Optimization and Control · Mathematics 2026-03-31 Xiaotian Jiang , Jiaxiang Li , Jiawen Bi , Mingyi Hong , Shuzhong Zhang

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…

Optimization and Control · Mathematics 2026-03-31 José A. Carrillo , Shi Jin , Haoyu Zhang , Yuhua Zhu

In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…

Optimization and Control · Mathematics 2025-01-20 Yuhao Wang , Seong-Hee Kim , Enlu Zhou

Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given…

Machine Learning · Computer Science 2023-06-21 Ankur Sinha , Satender Gunwal , Shivam Kumar

Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on…

Machine Learning · Statistics 2020-11-04 Michael Pearce , Janis Klaise , Matthew Groves

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…

Optimization and Control · Mathematics 2026-05-05 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo , Alain Zemkoho

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

Integrated learning and optimization (ILO) is a framework in contextual optimization which aims to train a predictive model for the probability distribution of the underlying problem data uncertainty, with the goal of enhancing the quality…

Optimization and Control · Mathematics 2026-01-26 Yuan Tao , Huifu Xu

In this paper, we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free…

Machine Learning · Computer Science 2026-03-02 Konstantin Riedl , Timo Klock , Carina Geldhauser , Massimo Fornasier

Consensus-based optimization (CBO) is a class of metaheuristic algorithms designed for global optimization problems. In the many-particle limit, classical CBO dynamics can be rigorously connected to mean-field equations that ensure…

Optimization and Control · Mathematics 2025-06-11 Jonathan Franceschi , Lorenzo Pareschi , Mattia Zanella

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…

Optimization and Control · Mathematics 2016-01-14 V. Jeyakumar , J. B. Lasserre , G. Li , T. S. Pham

Adam has become one of the most popular optimizers for training modern deep neural networks, such as transformers. However, its applicability is largely restricted to single-level optimization problems. In this paper, we aim to extend…

Machine Learning · Computer Science 2025-03-07 Xiaochuan Gong , Jie Hao , Mingrui Liu

Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with…

Optimization and Control · Mathematics 2025-12-01 Lesi Chen , Jingzhao Zhang

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its…

Optimization and Control · Mathematics 2023-06-05 Quanqi Hu , Zi-Hao Qiu , Zhishuai Guo , Lijun Zhang , Tianbao Yang

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

We propose Discrete Consensus-Based Optimization (DCBO), a fully discrete version of the Consensus-Based Optimization (CBO) framework. DCBO is a multi-agent method for the global optimization of possibly non-convex and non-differentiable…

Optimization and Control · Mathematics 2024-04-17 Junhyeok Byeon , Seung-Yeal Ha , Joong-Ho Won

Bilevel optimization (BLO) becomes fundamentally more challenging when the lower-level objective admits multiple minimizers. Beyond the unique-minimizer setting, two difficulties arise: (1) evaluating the hyper-objective $F_{\max}$ requires…

Optimization and Control · Mathematics 2026-03-16 Saeed Masiha , Zebang Shen , Negar Kiyavash , Niao He

Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…

Optimization and Control · Mathematics 2023-01-25 Yasmine Beck , Ivana Ljubić , Martin Schmidt

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