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Automated hyperparameter search in machine learning, especially for deep learning models, is typically formulated as a bilevel optimization problem, with hyperparameter values determined by the upper level and the model learning achieved by…

Machine Learning · Computer Science 2024-12-06 Meltem Apaydin Ustun , Liang Xu , Bo Zeng , Xiaoning Qian

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

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

Optimization and Control · Mathematics 2026-02-06 Mattia Solla , Johannes O. Royset

We investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…

Optimization and Control · Mathematics 2024-07-26 Leonardo Lozano , David Bergman , Andre Augusto Cire

Bilevel optimization, a hierarchical optimization paradigm, has gained significant attention in a wide range of practical applications, notably in the fine-tuning of generative models. However, due to the nested problem structure, most…

Optimization and Control · Mathematics 2025-07-29 Liuyuan Jiang , Quan Xiao , Lisha Chen , Tianyi Chen

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

Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…

Optimization and Control · Mathematics 2024-09-06 Sina Hajikazemi , Florian Steinke

Energy minimization methods are a classical tool in a multitude of computer vision applications. While they are interpretable and well-studied, their regularity assumptions are difficult to design by hand. Deep learning techniques on the…

Optimization and Control · Mathematics 2019-08-20 Jonas Geiping , Michael Moeller

In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly…

Optimization and Control · Mathematics 2026-04-03 Hang Xie , Xuewen Li , Peili Li , Qiuyu Wang

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…

Optimization and Control · Mathematics 2025-12-04 James Kotary , Himanshu Sharma , Ethan King , Draguna Vrabie , Ferdinando Fioretto , Jan Drgona

This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…

Optimization and Control · Mathematics 2012-05-30 Joseph W. Norman

We propose a bilevel optimization strategy for selecting the best hyperparameter value for the nonsmooth $\ell_p$ regularizer with $0<p\le 1$. The concerned bilevel optimization problem has a nonsmooth, possibly nonconvex,…

Optimization and Control · Mathematics 2021-12-20 Takayuki Okuno , Akiko Takeda , Akihiro Kawana , Motokazu Watanabe

We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with…

Optimization and Control · Mathematics 2026-02-06 Wei Shen , Jiawei Zhang , Minhui Huang , Cong Shen

Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…

Machine Learning · Computer Science 2021-08-03 Kaiyi Ji

Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given…

Machine Learning · Computer Science 2023-06-21 Ankur Sinha , Satender Gunwal , Shivam Kumar

This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…

Machine Learning · Computer Science 2023-01-27 Maziar Raissi

Learning approaches rely on hyperparameters that impact the algorithm's performance and affect the knowledge extraction process from data. Recently, Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a learning…

Numerical Analysis · Mathematics 2023-06-29 Nicoletta Del Buono , Flavia Esposito , Laura Selicato , Rafal Zdunek

A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as…

Optimization and Control · Mathematics 2016-11-04 Jiawang Nie , Li Wang , Jane Ye

Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…

Optimization and Control · Mathematics 2024-07-25 Bo Zhou , Ruiwei Jiang , Siqian Shen

Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…

Optimization and Control · Mathematics 2025-05-19 Xiaotian Jiang , Ioannis Tsaknakis , Prashant Khanduri , Mingyi Hong