English
Related papers

Related papers: Optimal Algorithms for Stochastic Bilevel Optimiza…

200 papers

Bilevel optimization has recently attracted significant attention in machine learning due to its wide range of applications and advanced hierarchical optimization capabilities. In this paper, we propose a plug-and-play framework, named…

Optimization and Control · Mathematics 2025-05-05 Tianshu Chu , Dachuan Xu , Wei Yao , Chengming Yu , Jin Zhang

Stochastic Bilevel Optimization has emerged as a fundamental framework for meta-learning and hyperparameter optimization. Despite the practical prevalence of single-loop algorithms--which update lower and upper variables concurrently--their…

Machine Learning · Computer Science 2026-03-02 Yubo Zhou , Luo Luo , Guang Dai , Haishan Ye

Bilevel optimization problems, encountered in fields such as economics, engineering, and machine learning, pose significant computational challenges due to their hierarchical structure and constraints at both upper and lower levels.…

Optimization and Control · Mathematics 2024-08-21 Mengwei Xu , Yu-Hong Dai , Xin-Wei Liu , Bo Wang

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

We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…

Optimization and Control · Mathematics 2025-11-25 Khanh-Hung Giang-Tran , Soroosh Shafiee , Nam Ho-Nguyen

Adam has become one of the most popular optimizers for training modern deep neural networks, such as transformers. However, its applicability is largely restricted to single-level optimization problems. In this paper, we aim to extend…

Machine Learning · Computer Science 2025-03-07 Xiaochuan Gong , Jie Hao , Mingrui Liu

This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…

Optimization and Control · Mathematics 2025-07-11 Rujun Jiang , Xu Shi , Weizheng Song , Jiulin Wang

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

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

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

This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of…

Optimization and Control · Mathematics 2026-05-08 Sheng Yang , Chengchang Liu , Lesi Chen , John C. S. Lui

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…

Optimization and Control · Mathematics 2024-02-13 Jeongyeol Kwon , Dohyun Kwon , Stephen Wright , Robert Nowak

In this paper, we develop two Riemannian stochastic smoothing algorithms for nonsmooth optimization problems on Riemannian manifolds, addressing distinct forms of the nonsmooth term \( h \). Both methods combine dynamic smoothing with a…

Optimization and Control · Mathematics 2025-05-27 Kangkang Deng , Zheng Peng , Weihe Wu

Stochastic bilevel optimization (SBO) is becoming increasingly essential in machine learning due to its versatility in handling nested structures. To address large-scale SBO, decentralized approaches have emerged as effective paradigms in…

Optimization and Control · Mathematics 2025-11-27 Boao Kong , Shuchen Zhu , Songtao Lu , Xinmeng Huang , Kun Yuan

This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such…

Machine Learning · Computer Science 2024-01-30 Wei Yao , Chengming Yu , Shangzhi Zeng , Jin Zhang

Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We…

Machine Learning · Statistics 2026-01-23 Jason Bohne , Ieva Petrulionyte , Michael Arbel , Julien Mairal , Paweł Polak

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

This paper analyzes a two-timescale stochastic algorithm framework for bilevel optimization. Bilevel optimization is a class of problems which exhibit a two-level structure, and its goal is to minimize an outer objective function with…

Optimization and Control · Mathematics 2022-06-09 Mingyi Hong , Hoi-To Wai , Zhaoran Wang , Zhuoran Yang

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

Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex…

Machine Learning · Computer Science 2025-11-27 Kaiyi Ji