English
Related papers

Related papers: Optimal Hessian/Jacobian-Free Nonconvex-PL Bilevel…

200 papers

Federated bilevel optimization has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel…

Machine Learning · Computer Science 2023-02-13 Minhui Huang , Dewei Zhang , Kaiyi Ji

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with…

Optimization and Control · Mathematics 2023-01-31 Xufeng Cai , Chaobing Song , Stephen J. Wright , Jelena Diakonikolas

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

Many important machine learning applications involve regularized nonconvex bi-level optimization. However, the existing gradient-based bi-level optimization algorithms cannot handle nonconvex or nonsmooth regularizers, and they suffer from…

Machine Learning · Computer Science 2022-06-06 Ziyi Chen , Bhavya Kailkhura , Yi Zhou

Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives…

Optimization and Control · Mathematics 2023-02-01 C. Yalçın Kaya , Helmut Maurer

Bilevel reinforcement learning (BRL) has emerged as a powerful framework for aligning generative models, yet its theoretical foundations, especially sample complexity bounds, remain underexplored. In this work, we present the first sample…

Machine Learning · Computer Science 2026-02-17 Mudit Gaur , Utsav Singh , Amrit Singh Bedi , Raghu Pasupathu , Vaneet Aggarwal

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…

Optimization and Control · Mathematics 2018-09-18 Yekini Shehu , Phan Tu Vuong , Alain Zemkoho

A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…

Optimization and Control · Mathematics 2018-12-05 Gernot Holler , Karl Kunisch , Richard C. Barnard

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 problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the…

Neural and Evolutionary Computing · Computer Science 2013-10-08 Ankur Sinha , Pekka Malo , Kalyanmoy Deb

In this work, we consider the bilevel optimization problem on Riemannian manifolds. We inspect the calculation of the hypergradient of such problems on general manifolds and thus enable the utilization of gradient-based algorithms to solve…

Optimization and Control · Mathematics 2024-02-09 Jiaxiang Li , Shiqian Ma

Computing tasks may often be posed as optimization problems. The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable. State-of-the-art methods for solving these problems typically only guarantee…

Optimization and Control · Mathematics 2022-10-11 Howard Heaton , Samy Wu Fung , Stanley Osher

We study a class of nonconvex-nonconcave minimax problems in which the inner maximization problem satisfies a local Kurdyka-Lojasiewicz (KL) condition that may vary with the outer minimization variable. In contrast to the global KL or…

Optimization and Control · Mathematics 2026-05-20 Zhaosong Lu , Xiangyuan Wang

This paper considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we…

Optimization and Control · Mathematics 2025-03-03 Lei Xu , Xinlei Yi , Jiayue Sun , Yang Shi , Karl H. Johansson , Tao Yang

Bilevel optimization problems consist of minimizing a value function whose evaluation depends on the solution of an inner optimization problem. These problems are typically tackled using first-order methods that require computing the…

Optimization and Control · Mathematics 2026-01-30 Marco Rando , Samuel Vaiter

Bilevel optimization with traffic equilibrium constraints plays an important role in transportation planning and management problems such as traffic control, transport network design, and congestion pricing. In this paper, we consider a…

Optimization and Control · Mathematics 2023-06-27 Akshit Goyal , Andrew Lamperski

Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…

Optimization and Control · Mathematics 2024-12-25 Quan Xiao , Tianyi Chen

Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables…

Optimization and Control · Mathematics 2024-11-04 Justin Dumouchelle , Esther Julien , Jannis Kurtz , Elias B. Khalil

Bi-level optimization model is able to capture a wide range of complex learning tasks with practical interest. Due to the witnessed efficiency in solving bi-level programs, gradient-based methods have gained popularity in the machine…

Optimization and Control · Mathematics 2021-06-16 Risheng Liu , Xuan Liu , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

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