English
Related papers

Related papers: Faster Gradient Methods for Highly-Smooth Stochast…

200 papers

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

This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…

Machine Learning · Computer Science 2025-12-16 Zhuanghua Liu , Luo Luo

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

Optimization and Control · Mathematics 2024-06-03 Jincheng Cao , Ruichen Jiang , Erfan Yazdandoost Hamedani , Aryan Mokhtari

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

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

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

Optimization and Control · Mathematics 2023-04-25 Ruichen Jiang , Nazanin Abolfazli , Aryan Mokhtari , Erfan Yazdandoost Hamedani

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

We present a method for solving general nonconvex-strongly-convex bilevel optimization problems. Our method -- the \emph{Restarted Accelerated HyperGradient Descent} (\texttt{RAHGD}) method -- finds an $\epsilon$-first-order stationary…

Optimization and Control · Mathematics 2023-07-04 Haikuo Yang , Luo Luo , Chris Junchi Li , Michael I. Jordan

This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…

Machine Learning · Computer Science 2025-01-16 Xiaochuan Gong , Jie Hao , Mingrui Liu

This paper studies the complexity of finding approximate stationary points for the smooth nonconvex-strongly-concave (NC-SC) saddle point problem: $\min_x\max_yf(x,y)$. Under the standard first-order smoothness conditions where $f$ is…

Optimization and Control · Mathematics 2024-12-10 Nuozhou Wang , Junyu Zhang , Shuzhong Zhang

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 design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…

Machine Learning · Computer Science 2020-06-25 Yossi Arjevani , Yair Carmon , John C. Duchi , Dylan J. Foster , Ayush Sekhari , Karthik Sridharan

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

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

We study the problem of finding an $\epsilon$-first-order stationary point (FOSP) of a smooth function, given access only to gradient information. The best-known gradient query complexity for this task, assuming both the gradient and…

Optimization and Control · Mathematics 2024-12-04 Ruichen Jiang , Aryan Mokhtari , Francisco Patitucci

Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}) parameters) to set step sizes, a…

Optimization and Control · Mathematics 2026-01-01 Xu Shi , Yinglin Du , Rufeng Xiao , Rujun Jiang

We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…

Optimization and Control · Mathematics 2019-06-05 Brian Bullins , Richard Peng

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

Stochastic Bilevel optimization usually involves minimizing an upper-level (UL) function that is dependent on the arg-min of a strongly-convex lower-level (LL) function. Several algorithms utilize Neumann series to approximate certain…

Optimization and Control · Mathematics 2023-06-22 Xuxing Chen , Tesi Xiao , Krishnakumar Balasubramanian
‹ Prev 1 2 3 10 Next ›