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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

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Machine Learning · Statistics 2024-12-10 Ieva Petrulionyte , Julien Mairal , Michael Arbel

Conventional learning methods simplify the bilinear model by regarding two intrinsically coupled factors independently, which degrades the optimization procedure. One reason lies in the insufficient training due to the asynchronous gradient…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Li'an Zhuo , Baochang Zhang , Linlin Yang , Hanlin Chen , Qixiang Ye , David Doermann , Guodong Guo , Rongrong Ji

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…

Optimization and Control · Mathematics 2025-06-10 Lea Bogensperger , Matthias J. Ehrhardt , Thomas Pock , Mohammad Sadegh Salehi , Hok Shing Wong

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

Optimization and Control · Mathematics 2019-12-17 Andreas Fischer , Alain B. Zemkoho , Shenglong Zhou

Bilevel optimization has found extensive applications in modern machine learning problems such as hyperparameter optimization, neural architecture search, meta-learning, etc. While bilevel problems with a unique inner minimal point (e.g.,…

Optimization and Control · Mathematics 2022-06-09 Daouda Sow , Kaiyi Ji , Ziwei Guan , Yingbin Liang

Bilevel optimization has been recently used in many machine learning problems such as hyperparameter optimization, policy optimization, and meta learning. Although many bilevel optimization methods have been proposed, they still suffer from…

Optimization and Control · Mathematics 2022-10-27 Feihu Huang , Junyi Li , Shangqian Gao , Heng Huang

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…

Optimization and Control · Mathematics 2025-05-06 Youran Dong , Junfeng Yang , Wei Yao , Jin Zhang

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…

Optimization and Control · Mathematics 2016-04-08 Xiaojun Chen , Zhaosong Lu , Ting Kei Pong

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…

Optimization and Control · Mathematics 2021-03-22 Yassine Laguel , Jérôme Malick , Wim Ackooij

Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…

Optimization and Control · Mathematics 2026-04-29 Lesi Chen , Jing Xu , Jingzhao Zhang

This paper considers a class of distributed bilevel optimization (DBO) problems with a coupled inner-level subproblem. Existing approaches typically rely on hypergradient estimations involving computationally expensive Hessian evaluation.…

Optimization and Control · Mathematics 2026-02-27 Youcheng Niu , Jinming Xu , Ying Sun , Li Chai , Jiming Chen

Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…

Optimization and Control · Mathematics 2025-04-25 Nazanin Abolfazli , Sina Sharifi , Mahyar Fazlyab , Erfan Yazdandoost Hamedani

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

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

Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…

Optimization and Control · Mathematics 2024-06-05 Wei Yao , Haian Yin , Shangzhi Zeng , Jin Zhang

This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The…

Optimization and Control · Mathematics 2019-04-03 Elias Salomão Helou , Lucas Eduardo Azevedo Simões

Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive…

Machine Learning · Computer Science 2020-07-23 Ankur Sinha , Tanmay Khandait , Raja Mohanty

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 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