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In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in…

Optimization and Control · Mathematics 2026-01-22 Sudkobfa Boontawee , Mootta Prangprakhon , Nimit Nimana

In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…

Optimization and Control · Mathematics 2025-01-20 Yuhao Wang , Seong-Hee Kim , Enlu Zhou

Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial warm restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient…

Machine Learning · Computer Science 2017-05-04 Ilya Loshchilov , Frank Hutter

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic…

Optimization and Control · Mathematics 2023-02-08 Zeeshan Akhtar , Amrit Singh Bedi , Srujan Teja Thomdapu , Ketan Rajawat

We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…

Optimization and Control · Mathematics 2025-11-25 Khanh-Hung Giang-Tran , Soroosh Shafiee , Nam Ho-Nguyen

Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…

Machine Learning · Computer Science 2022-06-07 Daouda Sow , Kaiyi Ji , Yingbin Liang

We study the zeroth-order query complexity of sampling from a general logconcave distribution: given access to an evaluation oracle for a convex function $V:\mathbb{R}^{d}\rightarrow\mathbb{R}\cup\{\infty\}$, output a point from a…

Statistics Theory · Mathematics 2026-04-03 Yunbum Kook , Santosh S. Vempala

Data augmentation is known to improve the generalization capabilities of neural networks, provided that the set of transformations is chosen with care, a selection often performed manually. Automatic data augmentation aims at automating…

Computer Vision and Pattern Recognition · Computer Science 2023-06-19 Juliette Marrie , Michael Arbel , Diane Larlus , Julien Mairal

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

In this paper we propose a sequential minimax optimization (SMO) method for solving a class of constrained bilevel optimization problems in which the lower-level part is a possibly nonsmooth convex optimization problem, while the…

Optimization and Control · Mathematics 2025-11-11 Zhaosong Lu , Sanyou Mei

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Optimization and Control · Mathematics 2018-05-01 James V. Burke , Frank E. Curtis , Adrian S. Lewis , Michael L. Overton , Lucas E. A. Simões

In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the…

Machine Learning · Computer Science 2020-07-03 Risheng Liu , Pan Mu , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

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

This article continues our study on simple bilevel and simple MPEC problems. In this article we focus on developing algorithms. We show how using the idea of a gap function one can represent a simple MPEC as a simple bilevel problem with…

Optimization and Control · Mathematics 2019-12-16 Stephan Dempe , Nguyen Dinh , Joydeep Dutta , Tanushree Pandit

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

Meta-learning algorithms for active learning are emerging as a promising paradigm for learning the ``best'' active learning strategy. However, current learning-based active learning approaches still require sufficient training data so as to…

Machine Learning · Computer Science 2019-09-10 Jingyu Shao , Qing Wang , Fangbing Liu

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

Optimization and Control · Mathematics 2024-02-01 Digvijay Boob , Qi Deng , Guanghui Lan

We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…

Optimization and Control · Mathematics 2025-09-29 Khanh-Hung Giang-Tran , Nam Ho-Nguyen , Fatma Kılınç-Karzan , Lingqing Shen

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

Optimization and Control · Mathematics 2026-01-12 Dimitris Boskos , Jorge Cortés , Sonia Martínez

We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…

Numerical Analysis · Mathematics 2023-08-04 Mo Zhou , Jiequn Han , Manas Rachh , Carlos Borges