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Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient…

Optimization and Control · Mathematics 2026-02-04 Qichao Cao , Shangzhi Zeng , Jin Zhang

We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…

Optimization and Control · Mathematics 2022-07-12 Michael Arbel , Julien Mairal

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

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

Optimization and Control · Mathematics 2015-06-12 Euhanna Ghadimi , Iman Shames , Mikael Johansson

The goal of coreset selection in supervised learning is to produce a weighted subset of data, so that training only on the subset achieves similar performance as training on the entire dataset. Existing methods achieved promising results in…

Machine Learning · Computer Science 2023-01-25 Xiao Zhou , Renjie Pi , Weizhong Zhang , Yong Lin , Tong Zhang

This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…

Optimization and Control · Mathematics 2023-06-08 Yue Xie , Stephen J. Wright

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

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…

Optimization and Control · Mathematics 2017-02-15 Shoham Sabach , Shimrit Shtern

This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…

Machine Learning · Computer Science 2025-12-16 Zhuanghua Liu , Luo Luo

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level…

Machine Learning · Computer Science 2026-05-15 Zhiyao Zhang , Myeung Suk Oh , Zhen Qin , Jiaxiang Li , Xin Zhang , Jia Liu

In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal…

Optimization and Control · Mathematics 2020-05-07 Yi Xu , Qihang Lin , Tianbao Yang

This paper studies the unconstrained nonconvex-strongly-convex bilevel optimization problem. A common approach to solving this problem is to alternately update the upper-level and lower-level variables using (biased) stochastic gradients or…

Optimization and Control · Mathematics 2025-03-18 Haimei Huo , Zhixun Su

We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…

Optimization and Control · Mathematics 2024-11-25 Dmitry Kovalev , Ekaterina Borodich

Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…

Optimization and Control · Mathematics 2025-11-25 Ajay Tak , Mayank Baranwal

We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…

Optimization and Control · Mathematics 2024-05-08 Ensio Suonperä , Tuomo Valkonen

We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…

Optimization and Control · Mathematics 2016-04-27 Peter Ochs , René Ranftl , Thomas Brox , Thomas Pock

As neural networks grow deeper and wider, learning networks with hard-threshold activations is becoming increasingly important, both for network quantization, which can drastically reduce time and energy requirements, and for creating large…

Machine Learning · Computer Science 2018-04-18 Abram L. Friesen , Pedro Domingos

Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…

Machine Learning · Computer Science 2026-04-07 Xuelin Zhang , Hong Chen , Bin Gu , Tieliang Gong , Feng Zheng

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…

Machine Learning · Computer Science 2024-12-25 Omer Ekmekcioglu , Nursen Aydin , Juergen Branke

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…

Machine Learning · Computer Science 2019-04-09 Amirreza Shaban , Ching-An Cheng , Nathan Hatch , Byron Boots