English
Related papers

Related papers: First-Order Methods for Linearly Constrained Bilev…

200 papers

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

In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $\epsilon$-stationary point within…

Optimization and Control · Mathematics 2026-05-26 Lesi Chen , Yaohua Ma , 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

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…

Optimization and Control · Mathematics 2026-05-11 Yiyang Shen , Yutian He , Weiran Wang , Qihang Lin

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…

Optimization and Control · Mathematics 2023-01-27 Jeongyeol Kwon , Dohyun Kwon , Stephen Wright , Robert Nowak

Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is…

Machine Learning · Computer Science 2025-12-03 Zihao Zhao , Kai-Chia Mo , Shing-Hei Ho , Brandon Amos , Kai Wang

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

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

We study bilevel optimization with a fixed polyhedral lower feasible set. Such problems are challenging for two reasons: active-set changes can make the upper objective nonsmooth, and existing hypergradient methods typically require…

Optimization and Control · Mathematics 2026-05-13 Tenglong Hong , Paul Grigas

We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…

Optimization and Control · Mathematics 2020-11-19 Abraham P. Vinod , Arie Israel , Ufuk Topcu

In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…

Optimization and Control · Mathematics 2023-08-16 Jincheng Cao , Ruichen Jiang , Nazanin Abolfazli , Erfan Yazdandoost Hamedani , Aryan Mokhtari

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

Optimization and Control · Mathematics 2024-03-15 Nazanin Abolfazli , Ruichen Jiang , Aryan Mokhtari , Erfan Yazdandoost Hamedani

This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve…

Optimization and Control · Mathematics 2026-04-17 Qi Deng , Guanghui Lan , Zhenwei Lin

In this work, we study nonconvex-strongly convex online bilevel optimization (OBO) using only first-order oracle. Existing OBO algorithms are mainly based on hypergradient descent, which requires access to a Hessian-vector product (HVP)…

Machine Learning · Computer Science 2026-05-12 Tingkai Jia , Cheng Chen

We consider the problem of finding stationary points in Bilevel optimization when the lower-level problem is unconstrained and strongly convex. The problem has been extensively studied in recent years; the main technical challenge is to…

Optimization and Control · Mathematics 2024-02-13 Jeongyeol Kwon , Dohyun Kwon , Hanbaek Lyu

First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…

Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta-learning, continual learning, and reinforcement learning. Conventional BO…

Machine Learning · Computer Science 2022-09-20 Mao Ye , Bo Liu , Stephen Wright , Peter Stone , Qiang Liu

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

Simple bilevel problems are optimization problems in which we want to find an optimal solution to an inner problem that minimizes an outer objective function. Such problems appear in many machine learning and signal processing applications…

Optimization and Control · Mathematics 2022-12-21 Lior Doron , Shimrit Shtern

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

Optimization and Control · Mathematics 2021-01-07 Pavel Dvurechensky , Mathias Staudigl , Shimrit Shtern
‹ Prev 1 2 3 10 Next ›