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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

We study the feature-based newsvendor problem, in which a decision-maker has access to historical data consisting of demand observations and exogenous features. In this setting, we investigate feature selection, aiming to derive sparse,…

Machine Learning · Computer Science 2022-09-13 Breno Serrano , Stefan Minner , Maximilian Schiffer , Thibaut Vidal

This review discusses methods for learning parameters for image reconstruction problems using bilevel formulations. Image reconstruction typically involves optimizing a cost function to recover a vector of unknown variables that agrees with…

Optimization and Control · Mathematics 2022-06-16 Caroline Crockett , Jeffrey A. Fessler

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

Optimization and Control · Mathematics 2025-04-16 Yunier Bello-Cruz , Max L. N. Gonçalves , Jefferson G. Melo , Cassandra Mohr

Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model…

Machine Learning · Computer Science 2022-10-18 Kartik Chandra , Audrey Xie , Jonathan Ragan-Kelley , Erik Meijer

This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…

Optimization and Control · Mathematics 2025-11-18 Cac Phan , Kai Wang

This paper investigates two inexact Levenberg-Marquardt (LM) methods for solving systems of nonlinear equations. Both approaches compute approximate search directions by solving the LM linear system inexactly, subject to specific…

Optimization and Control · Mathematics 2025-07-23 Bas Symoens , Morteza Rahimi , Masoud Ahookhosh

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

Optimization and Control · Mathematics 2016-05-02 Masoud Ahookhosh

In the development of first-order methods for smooth (resp., composite) convex optimization problems, where smooth functions with Lipschitz continuous gradients are minimized, the gradient (resp., gradient mapping) norm becomes a…

Optimization and Control · Mathematics 2020-10-06 Masaru Ito , Mituhiro Fukuda

Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…

Optimization and Control · Mathematics 2018-09-27 Harshal Kaushik , Farzad Yousefian

Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…

Machine Learning · Computer Science 2024-11-05 Xiaoyu Wang , Rui Pan , Renjie Pi , Jipeng Zhang

We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…

Optimization and Control · Mathematics 2024-12-23 Rajiv Sambharya , Bartolomeo Stellato

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size.…

Machine Learning · Computer Science 2021-09-14 Majid Jahani , Sergey Rusakov , Zheng Shi , Peter Richtárik , Michael W. Mahoney , Martin Takáč

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

Machine Learning · Statistics 2020-07-13 Riccardo Grazzi , Luca Franceschi , Massimiliano Pontil , Saverio Salzo

Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on…

Optimization and Control · Mathematics 2025-10-14 Abbas Khademi , Antonio Silveti-Falls

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

Optimization and Control · Mathematics 2022-12-14 Thang Tran Ngoc , Hai Trinh Ngoc

Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…

Optimization and Control · Mathematics 2024-04-24 Youran Dong , Shiqian Ma , Junfeng Yang , Chao Yin

A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…

Optimization and Control · Mathematics 2018-12-05 Gernot Holler , Karl Kunisch , Richard C. Barnard

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting…

Machine Learning · Computer Science 2019-03-08 Matthew MacKay , Paul Vicol , Jon Lorraine , David Duvenaud , Roger Grosse

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

Machine Learning · Computer Science 2019-12-06 Gauthier Gidel , Francis Bach , Simon Lacoste-Julien