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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

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

Alternating structure-adapted proximal (ASAP) gradient algorithm (M. Nikolova and P. Tan, SIAM J Optim, 29:2053-2078, 2019) has drawn much attention due to its efficiency in solving nonconvex nonsmooth optimization problems. However, the…

Optimization and Control · Mathematics 2024-06-26 Ying Gao , Chunfeng Cui , Wenxing Zhang , Deren Han

Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…

Machine Learning · Computer Science 2024-11-05 Xiaoyu Wang , Rui Pan , Renjie Pi , Jipeng Zhang

Due to their simplicity and excellent performance, parallel asynchronous variants of stochastic gradient descent have become popular methods to solve a wide range of large-scale optimization problems on multi-core architectures. Yet,…

Optimization and Control · Mathematics 2017-11-07 Fabian Pedregosa , Rémi Leblond , Simon Lacoste-Julien

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…

Optimization and Control · Mathematics 2021-06-16 Prashant Khanduri , Siliang Zeng , Mingyi Hong , Hoi-To Wai , Zhaoran Wang , Zhuoran Yang

We develop new algorithms for Riemannian bilevel optimization. We focus in particular on batch and stochastic gradient-based methods, with the explicit goal of avoiding second-order information such as Riemannian hyper-gradients. We propose…

Optimization and Control · Mathematics 2024-05-28 Sanchayan Dutta , Xiang Cheng , Suvrit Sra

In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…

Optimization and Control · Mathematics 2025-03-14 Xiaotian Jiang , Jiaxiang Li , Mingyi Hong , Shuzhong Zhang

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

Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…

Optimization and Control · Mathematics 2023-01-25 Yasmine Beck , Ivana Ljubić , Martin Schmidt

In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…

Optimization and Control · Mathematics 2021-06-28 Anton Rodomanov , Yurii Nesterov

Stochastic bilevel optimization tackles challenges involving nested optimization structures. Its fast-growing scale nowadays necessitates efficient distributed algorithms. In conventional distributed bilevel methods, each worker must…

Optimization and Control · Mathematics 2024-05-30 Yutong He , Jie Hu , Xinmeng Huang , Songtao Lu , Bin Wang , Kun Yuan

Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

Optimization and Control · Mathematics 2025-05-20 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

Alignment of Large Language Models (LLMs) typically relies on Reinforcement Learning from Human Feedback (RLHF) with gradient-based optimizers such as Proximal Policy Optimization (PPO) or Group Relative Policy Optimization (GRPO). While…

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

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning and vision fields. The validity of existing works heavily relies on solving a series of approximation subproblems with extraordinarily high…

Optimization and Control · Mathematics 2022-05-23 Risheng Liu , Xuan Liu , Wei Yao , Shangzhi Zeng , Jin Zhang

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

This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These…

Optimization and Control · Mathematics 2024-05-17 Risheng Liu , Zhu Liu , Wei Yao , Shangzhi Zeng , Jin Zhang

In this paper, we study and analyze zeroth-order stochastic approximation algorithms for solving bilvel problems, when neither the upper/lower objective values, nor their unbiased gradient estimates are available. In particular, exploiting…

Optimization and Control · Mathematics 2024-04-02 Alireza Aghasi , Saeed Ghadimi

Smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems. In this note we synthesize…

Optimization and Control · Mathematics 2012-09-03 James V. Burke , Tim Hoheisel