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Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…

Optimization and Control · Mathematics 2019-11-27 Chin Pang Ho , Michal Kocvara , Panos Parpas

Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…

Machine Learning · Computer Science 2024-10-14 Bowei Zhu , Shaojie Li , Yong Liu

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision…

Optimization and Control · Mathematics 2023-10-31 Yifan Hu , Jie Wang , Yao Xie , Andreas Krause , Daniel Kuhn

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

Optimization and Control · Mathematics 2024-11-05 Andi Han , Bamdev Mishra , Pratik Jawanpuria , Akiko Takeda

Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community including hyperparameter optimization and meta-knowledge extraction. Bi-level optimization embeds one problem within another…

Machine Learning · Computer Science 2023-07-11 Can Chen , Xi Chen , Chen Ma , Zixuan Liu , Xue Liu

We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a…

Optimization and Control · Mathematics 2024-04-30 Allahkaram Shafiei , Vyacheslav Kungurtsev , Jakub Marecek

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…

Machine Learning · Computer Science 2021-12-17 Junjie Yang , Kaiyi Ji , Yingbin Liang

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

Machine Learning · Computer Science 2015-07-28 Elad Hazan , Kfir Y. Levy , Shai Shalev-Shwartz

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

Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…

Optimization and Control · Mathematics 2025-10-13 Hantao Nie , Jiaxiang Li , Zaiwen Wen

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

Machine Learning · Computer Science 2024-10-16 Yuntian Gu , Xuzheng Chen

Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…

Optimization and Control · Mathematics 2017-09-27 Aurélien Ouattara , Anil Aswani

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

Optimization and Control · Mathematics 2019-12-17 Andreas Fischer , Alain B. Zemkoho , Shenglong Zhou

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Machine Learning · Statistics 2024-12-10 Ieva Petrulionyte , Julien Mairal , Michael Arbel

Bilevel optimization, a well-established field for modeling hierarchical decision-making problems, has recently intersected with sustainability studies and practices, resulting in a series of works focusing on bilevel optimization problems…

Optimization and Control · Mathematics 2026-04-07 Giulia Caselli , Manuel Iori , Ivana Ljubić

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

Machine Learning · Computer Science 2017-07-06 Jakub Konečný

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

Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…

Machine Learning · Computer Science 2025-10-27 Xiaochuan Gong , Jie Hao , Mingrui Liu

The growing size of available data has attracted increasing interest in solving minimax problems in a decentralized manner for various machine learning tasks. Previous theoretical research has primarily focused on the convergence rate and…

Machine Learning · Computer Science 2023-11-01 Miaoxi Zhu , Li Shen , Bo Du , Dacheng Tao

Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…

Optimization and Control · Mathematics 2025-04-25 Nazanin Abolfazli , Sina Sharifi , Mahyar Fazlyab , Erfan Yazdandoost Hamedani