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Two-level stochastic optimization formulations have become instrumental in a number of machine learning contexts such as continual learning, neural architecture search, adversarial learning, and hyperparameter tuning. Practical stochastic…

Optimization and Control · Mathematics 2023-11-08 Tommaso Giovannelli , Griffin Dean Kent , Luis Nunes Vicente

We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…

Optimization and Control · Mathematics 2021-11-08 Jonathan Kelner , Annie Marsden , Vatsal Sharan , Aaron Sidford , Gregory Valiant , Honglin Yuan

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

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…

Machine Learning · Computer Science 2023-03-16 Meng Ding , Mingxi Lei , Yunwen Lei , Di Wang , Jinhui Xu

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

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

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Optimization and Control · Mathematics 2025-04-08 Prashant Khanduri , Ioannis Tsaknakis , Yihua Zhang , Sijia Liu , Mingyi Hong

This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…

Optimization and Control · Mathematics 2025-11-06 Dhaval Pujara , Ankur Sinha

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 investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…

Machine Learning · Computer Science 2025-01-16 Xiaochuan Gong , Jie Hao , Mingrui Liu

This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The…

Optimization and Control · Mathematics 2019-04-03 Elias Salomão Helou , Lucas Eduardo Azevedo Simões

In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming…

Optimization and Control · Mathematics 2025-04-17 Stephan Dempe , Joydeep Duta , Tanushree Pandit , K. S. Mallikarjuna Rao

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…

Machine Learning · Statistics 2018-07-04 Luca Franceschi , Paolo Frasconi , Saverio Salzo , Riccardo Grazzi , Massimilano Pontil

We analyze stochastic conditional gradient methods for constrained optimization problems arising in over-parametrized machine learning. We show that one could leverage the interpolation-like conditions satisfied by such models to obtain…

Optimization and Control · Mathematics 2022-01-28 Tesi Xiao , Krishnakumar Balasubramanian , Saeed Ghadimi

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…

Optimization and Control · Mathematics 2021-03-22 Yassine Laguel , Jérôme Malick , Wim Ackooij

A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…

Optimization and Control · Mathematics 2017-05-09 Ankur Sinha , Zhichao Lu , Kalyanmoy Deb , Pekka Malo

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

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

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Optimization and Control · Mathematics 2022-02-16 Meng Li , Paul Grigas , Alper Atamturk

In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…

Optimization and Control · Mathematics 2024-11-13 Jiajia Yu , Quan Xiao , Tianyi Chen , Rongjie Lai