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In this paper, we present difference of convex algorithms for solving bilevel programs in which the upper level objective functions are difference of convex functions, and the lower level programs are fully convex. This nontrivial class of…

Optimization and Control · Mathematics 2022-08-30 Jane J. Ye , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

In this paper, we focus on the nonconvex-nonconvex bilevel optimization problem (BLO), where both upper-level and lower-level objectives are nonconvex, with the upper-level problem potentially being nonsmooth. We develop a two-timescale…

Optimization and Control · Mathematics 2026-04-24 Nachuan Xiao , Xiaoyin Hu , Xin Liu , Kim-Chuan Toh

Bilevel optimization (BLO) is a popular approach with many applications including hyperparameter optimization, neural architecture search, adversarial robustness and model-agnostic meta-learning. However, the approach suffers from time and…

Machine Learning · Computer Science 2021-06-08 Valerii Likhosherstov , Xingyou Song , Krzysztof Choromanski , Jared Davis , Adrian Weller

Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on…

Machine Learning · Computer Science 2025-11-18 Fares El Khoury , Edouard Pauwels , Samuel Vaiter , Michael Arbel

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

Bilevel programming has recently received attention in the literature due to its wide range of applications, including reinforcement learning and hyper-parameter optimization. However, it is widely assumed that the underlying bilevel…

Machine Learning · Computer Science 2024-10-11 Parvin Nazari , Ahmad Mousavi , Davoud Ataee Tarzanagh , George Michailidis

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

Bilevel optimization (BLO) offers a principled framework for hierarchical decision-making and has been widely applied in machine learning tasks such as hyperparameter optimization and meta-learning. While existing BLO methods are mostly…

Optimization and Control · Mathematics 2025-10-20 Zhuo Chen , Xinjian Xu , Shihui Ying , Tieyong Zeng

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision…

Optimization and Control · Mathematics 2023-10-31 Yifan Hu , Jie Wang , Yao Xie , Andreas Krause , Daniel Kuhn

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

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

Machine Learning · Computer Science 2024-10-16 Yuntian Gu , Xuzheng Chen

Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point -- a stationary point of the hyper-objective function obtained by minimizing or maximizing…

Optimization and Control · Mathematics 2025-10-30 He Chen , Jiajin Li , Anthony Man-Cho So

With the development of large-scale models, traditional distributed bilevel optimization algorithms cannot be applied directly in low-resource clients. The key reason lies in the excessive computation involved in optimizing both the lower-…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-01 Mingyi Li , Xiao Zhang , Ruisheng Zheng , Hongjian Shi , Yuan Yuan , Xiuzhen Cheng , Dongxiao Yu

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

Optimization and Control · Mathematics 2025-11-14 Ilyas Fatkhullin , Niao He , Guanghui Lan , Florian Wolf

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

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

As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a…

Machine Learning · Computer Science 2025-11-12 Zhiyao Zhang , Zhuqing Liu , Xin Zhang , Wen-Yen Chen , Jiyan Yang , Jia Liu

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

In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…

Optimization and Control · Mathematics 2021-07-14 Masoud Ahookhosh , Yurii Nesterov

Bilevel optimization is one of the fundamental problems in machine learning and optimization. Recent theoretical developments in bilevel optimization focus on finding the first-order stationary points for nonconvex-strongly-convex cases. In…

Machine Learning · Computer Science 2023-05-11 Minhui Huang , Xuxing Chen , Kaiyi Ji , Shiqian Ma , Lifeng Lai