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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

Strongly motivated from use in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the recent advance of algorithms for solving problems with nonsmooth…

Optimization and Control · Mathematics 2023-04-21 Jan Harold Alcantara , Chieu Thanh Nguyen , Takayuki Okuno , Akiko Takeda , Jein-Shan Chen

Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with…

Optimization and Control · Mathematics 2025-12-01 Lesi Chen , Jingzhao Zhang

In this paper, we focus on the nonconvex-strongly-convex bilevel optimization problem (BLO). In this BLO, the objective function of the upper-level problem is nonconvex and possibly nonsmooth, and the lower-level problem is smooth and…

Optimization and Control · Mathematics 2022-12-26 Xiaoyin Hu , Nachuan Xiao , Xin Liu , Kim-Chuan Toh

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

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 optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Optimization and Control · Mathematics 2025-11-11 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…

Optimization and Control · Mathematics 2018-09-27 Mostafa Amini , Farzad Yousefian

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

Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…

Machine Learning · Computer Science 2023-03-28 Hongchang Gao , Bin Gu , My T. Thai

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

Optimization and Control · Mathematics 2020-05-05 Quoc Tran-Dinh , Nhan H. Pham , Dzung T. Phan , Lam M. Nguyen

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

We develop and analyze stochastic approximation algorithms for solving nested compositional bi-level optimization problems. These problems involve a nested composition of $T$ potentially non-convex smooth functions in the upper-level, and a…

Optimization and Control · Mathematics 2023-07-12 Xuxing Chen , Krishnakumar Balasubramanian , Saeed Ghadimi

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine…

Machine Learning · Computer Science 2026-05-26 Xinwen Zhang , Yihan Zhang , Heng Liang , Hongchang Gao

Bilevel optimization has arisen as a powerful tool for solving a variety of machine learning problems. Two current popular bilevel optimizers AID-BiO and ITD-BiO naturally involve solving one or two sub-problems, and consequently, whether…

Machine Learning · Computer Science 2022-06-02 Kaiyi Ji , Mingrui Liu , Yingbin Liang , Lei Ying

Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…

Optimization and Control · Mathematics 2025-03-25 Sina Sharifi , Nazanin Abolfazli , Erfan Yazdandoost Hamedani , Mahyar Fazlyab

While variance reduction methods have shown great success in solving large scale optimization problems, many of them suffer from accumulated errors and, therefore, should periodically require the full gradient computation. In this paper, we…

Machine Learning · Computer Science 2022-10-05 Kazusato Oko , Shunta Akiyama , Tomoya Murata , Taiji Suzuki

It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower…

Optimization and Control · Mathematics 2023-05-04 Yasmine Beck , Daniel Bienstock , Martin Schmidt , Johannes Thürauf

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…

Machine Learning · Computer Science 2023-03-16 Meng Ding , Mingxi Lei , Yunwen Lei , Di Wang , Jinhui Xu

In recent years, decentralized bilevel optimization problems have received increasing attention in the networking and machine learning communities thanks to their versatility in modeling decentralized learning problems over peer-to-peer…

Machine Learning · Computer Science 2022-10-07 Zhuqing Liu , Xin Zhang , Prashant Khanduri , Songtao Lu , Jia Liu