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We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…

Optimization and Control · Mathematics 2023-11-20 Sepideh Samadi , Daniel Burbano , Farzad Yousefian

We propose a framework for online meta-optimization of parameters that govern optimization, called Amortized Proximal Optimization (APO). We first interpret various existing neural network optimizers as approximate stochastic proximal point…

Machine Learning · Computer Science 2022-03-02 Juhan Bae , Paul Vicol , Jeff Z. HaoChen , Roger Grosse

Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…

Optimization and Control · Mathematics 2019-11-01 Maher Nouiehed , Maziar Sanjabi , Tianjian Huang , Jason D. Lee , Meisam Razaviyayn

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…

Machine Learning · Computer Science 2021-12-17 Junjie Yang , Kaiyi Ji , Yingbin Liang

First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…

Optimization and Control · Mathematics 2024-02-07 Junyu Zhang , Mingyi Hong

Bi-level optimization (BO) has become a fundamental mathematical framework for addressing hierarchical machine learning problems. As deep learning models continue to grow in size, the demand for scalable bi-level optimization solutions has…

Machine Learning · Computer Science 2024-12-25 Qianli Shen , Yezhen Wang , Zhouhao Yang , Xiang Li , Haonan Wang , Yang Zhang , Jonathan Scarlett , Zhanxing Zhu , Kenji Kawaguchi

With the development of large-scale models, traditional distributed bilevel optimization algorithms cannot be applied directly in low-resource clients. The key reason lies in the excessive computation involved in optimizing both the lower-…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-01 Mingyi Li , Xiao Zhang , Ruisheng Zheng , Hongjian Shi , Yuan Yuan , Xiuzhen Cheng , Dongxiao Yu

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

In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper-…

Optimization and Control · Mathematics 2025-08-01 Jincheng Cao , Ruichen Jiang , Erfan Yazdandoost Hamedani , Aryan Mokhtari

Recent advances in computationally efficient non-myopic Bayesian optimization (BO) improve query efficiency over traditional myopic methods like expected improvement while only modestly increasing computational cost. These advances have…

Machine Learning · Statistics 2021-12-07 Yunxiang Zhang , Xiangyu Zhang , Peter I. Frazier

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

Optimization and Control · Mathematics 2026-04-07 Donald Goldfarb , Lexiao Lai , Tianyi Lin , Jiayu 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

Stochastic minimax optimization on Riemannian manifolds has recently attracted significant attention due to its broad range of applications, such as robust training of neural networks and robust maximum likelihood estimation. Existing…

Optimization and Control · Mathematics 2026-02-11 Hongye Wang , Chang He , Bo Jiang

Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…

Optimization and Control · Mathematics 2023-08-01 G. V. Aivazian , F. S. Stonyakin , D. A. Pasechnyuk , M. S. Alkousa , A. M. Raigorodskii

Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…

Optimization and Control · Mathematics 2025-01-17 Zhichao Jia , Benjamin Grimmer

Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…

Optimization and Control · Mathematics 2025-10-08 Zilong Ye , Shiqian Ma , Junfeng Yang , Danqing Zhou

This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…

Optimization and Control · Mathematics 2025-10-28 Yijin Ren , Haifeng Xu , Qi Deng

This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…

Optimization and Control · Mathematics 2025-02-05 Nguyen Duc Anh , Tran Ngoc Thang

In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…

Optimization and Control · Mathematics 2025-11-10 Qiankun Shi , Xiao Wang

This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…

Optimization and Control · Mathematics 2021-12-28 Weiwei Kong