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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

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning and vision fields. The validity of existing works heavily relies on solving a series of approximation subproblems with extraordinarily high…

Optimization and Control · Mathematics 2022-05-23 Risheng Liu , Xuan Liu , Wei Yao , Shangzhi Zeng , Jin Zhang

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…

Optimization and Control · Mathematics 2024-02-13 Jeongyeol Kwon , Dohyun Kwon , Stephen Wright , Robert Nowak

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

Optimization and Control · Mathematics 2023-04-25 Ruichen Jiang , Nazanin Abolfazli , Aryan Mokhtari , Erfan Yazdandoost Hamedani

Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…

Optimization and Control · Mathematics 2026-05-28 Eduardo Nolasco , Ross D. King , Vassilios S. Vassiliadis

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

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

We consider a generic min-max multi-objective bilevel optimization problem with applications in robust machine learning such as representation learning and hyperparameter optimization. We design MORBiT, a novel single-loop gradient…

Machine Learning · Computer Science 2023-03-08 Alex Gu , Songtao Lu , Parikshit Ram , Lily Weng

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

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

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

Optimization and Control · Mathematics 2025-01-28 Huaqing Zhang , Lesi Chen , Jing Xu , Jingzhao Zhang

Bilevel optimization (BLO) offers a principled framework for hierarchical decision-making and has been widely applied in machine learning tasks such as hyperparameter optimization and meta-learning. While existing BLO methods are mostly…

Optimization and Control · Mathematics 2025-10-20 Zhuo Chen , Xinjian Xu , Shihui Ying , Tieyong Zeng

In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper-…

Optimization and Control · Mathematics 2025-08-01 Jincheng Cao , Ruichen Jiang , Erfan Yazdandoost Hamedani , Aryan Mokhtari

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…

Machine Learning · Computer Science 2024-01-19 Jie Hao , Xiaochuan Gong , Mingrui Liu

In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual…

Optimization and Control · Mathematics 2022-11-22 Quanqi Hu , Yongjian Zhong , Tianbao Yang

In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…

Optimization and Control · Mathematics 2026-03-24 Edoardo Cesaroni , Giampaolo Liuzzi , Stefano Lucidi

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

Optimization and Control · Mathematics 2024-03-15 Nazanin Abolfazli , Ruichen Jiang , Aryan Mokhtari , Erfan Yazdandoost Hamedani

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 study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…

Optimization and Control · Mathematics 2023-08-16 Jincheng Cao , Ruichen Jiang , Nazanin Abolfazli , Erfan Yazdandoost Hamedani , Aryan Mokhtari

Bilevel optimization has recently attracted growing interests due to its wide applications in modern machine learning problems. Although recent studies have characterized the convergence rate for several such popular algorithms, it is still…

Machine Learning · Computer Science 2022-02-01 Kaiyi Ji , Yingbin Liang