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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 problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…

Optimization and Control · Mathematics 2024-07-15 Mathieu Besançon , Miguel F. Anjos , Luce Brotcorne

Bi-level optimization (BO) has become a fundamental mathematical framework for addressing hierarchical machine learning problems. As deep learning models continue to grow in size, the demand for scalable bi-level optimization solutions has…

Machine Learning · Computer Science 2024-12-25 Qianli Shen , Yezhen Wang , Zhouhao Yang , Xiang Li , Haonan Wang , Yang Zhang , Jonathan Scarlett , Zhanxing Zhu , Kenji Kawaguchi

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

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…

Optimization and Control · Mathematics 2021-04-20 Geunyeong Byeon , Pascal Van Hentenryck

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

The construction of machine learning models involves many bi-level multi-objective optimization problems (BL-MOPs), where upper level (UL) candidate solutions must be evaluated via training weights of a model in the lower level (LL). Due to…

Neural and Evolutionary Computing · Computer Science 2023-02-07 Chao Wang , Licheng Jiao , Jiaxuan Zhao , Lingling Li , Xu Liu , Fang Liu , Shuyuan Yang

Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering. It automates the design of an optimization method based on…

Optimization and Control · Mathematics 2021-07-05 Tianlong Chen , Xiaohan Chen , Wuyang Chen , Howard Heaton , Jialin Liu , Zhangyang Wang , Wotao Yin

In this paper, we focus on the nonconvex-nonconvex bilevel optimization problem (BLO), where both upper-level and lower-level objectives are nonconvex, with the upper-level problem potentially being nonsmooth. We develop a two-timescale…

Optimization and Control · Mathematics 2026-04-24 Nachuan Xiao , Xiaoyin Hu , Xin Liu , Kim-Chuan Toh

Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…

Optimization and Control · Mathematics 2026-03-23 Nagisa Sugishita , Margarida Carvalho

Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired…

Bilevel optimization has recently attracted significant attention in machine learning due to its wide range of applications and advanced hierarchical optimization capabilities. In this paper, we propose a plug-and-play framework, named…

Optimization and Control · Mathematics 2025-05-05 Tianshu Chu , Dachuan Xu , Wei Yao , Chengming Yu , Jin Zhang

This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…

Optimization and Control · Mathematics 2025-07-11 Rujun Jiang , Xu Shi , Weizheng Song , Jiulin Wang

Collaborative learning is an important tool to train multiple clients more effectively by enabling communication among clients. Identifying helpful clients, however, presents challenging and often introduces significant overhead. In this…

Machine Learning · Computer Science 2024-09-10 Diba Hashemi , Lie He , Martin Jaggi

Black-box optimization (BBO) addresses problems where objectives are accessible only through costly queries without gradients or explicit structure. Classical derivative-free methods -- line search, direct search, and model-based solvers…

Machine Learning · Computer Science 2025-10-01 Morteza Kimiaei , Vyacheslav Kungurtsev

Penalty-based methods have become popular for solving bilevel optimization (BLO) problems, thanks to their effective first-order nature. However, they often require inner-loop iterations to solve the lower-level (LL) problem and small…

Optimization and Control · Mathematics 2025-11-24 Liuyuan Jiang , Quan Xiao , Lisha Chen , Tianyi Chen

Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…

Optimization and Control · Mathematics 2024-09-06 Sina Hajikazemi , Florian Steinke

In this paper we propose a sequential minimax optimization (SMO) method for solving a class of constrained bilevel optimization problems in which the lower-level part is a possibly nonsmooth convex optimization problem, while the…

Optimization and Control · Mathematics 2025-11-11 Zhaosong Lu , Sanyou Mei

Low-rank adaptation (LoRA) is a popular method for fine-tuning large-scale pre-trained models in downstream tasks by learning low-rank incremental matrices. Though LoRA and its variants effectively reduce the number of trainable parameters…

Machine Learning · Computer Science 2024-03-21 Rushi Qiang , Ruiyi Zhang , Pengtao Xie

Several important problem settings within the literature of reinforcement learning (RL), such as meta-learning, hierarchical learning, and RL from human feedback (RL-HF), can be modelled as bilevel RL problems. A lot has been achieved in…

Machine Learning · Computer Science 2026-02-03 Naman Saxena , Vaneet Aggarwal