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In this paper, we consider constrained optimization problems with convex, smooth objective and constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class…

Optimization and Control · Mathematics 2024-12-03 Nitesh Kumar Singh , Ion Necoara

This paper focuses on decentralized stochastic bilevel optimization (DSBO) where agents only communicate with their neighbors. We propose Decentralized Stochastic Gradient Descent and Ascent with Gradient Tracking (DSGDA-GT), a novel…

Optimization and Control · Mathematics 2026-01-06 Xiaoyu Wang , Xuxing Chen , Shiqian Ma , Tong Zhang

We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…

Machine Learning · Computer Science 2020-10-22 Kaiwen Zhou , Anthony Man-Cho So , James Cheng

An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…

Optimization and Control · Mathematics 2026-05-11 Yunlang Zhu , Lingjun Guo , Zahra Khatti , Xiaoyi Qu , Chia-Yuan Wu , Lara Zebiane , Frank E. Curtis

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…

Machine Learning · Computer Science 2025-08-08 Ashok Cutkosky , Harsh Mehta , Francesco Orabona

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

Optimization and Control · Mathematics 2016-09-27 Xiantao Xiao , Yongfeng Li , Zaiwen Wen , Liwei Zhang

We propose a first-order method for stochastic strongly convex optimization that attains $O(1/n)$ rate of convergence, analysis show that the proposed method is simple, easily to implement, and in worst case, asymptotically four times…

Optimization and Control · Mathematics 2011-10-14 Peng Cheng

This paper considers coordinated linear precoding in downlink multicell multiuser orthogonal frequency-division multiple access (OFDMA) network. A less-complex, fast and provably convergent algorithm that maximizes the weighted sum-rate…

Information Theory · Computer Science 2017-08-17 Mirza Golam Kibria , Hidekazu Murata , Susumu Yoshida

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

We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order…

Optimization and Control · Mathematics 2021-10-27 Aurelien Lucchi , Antonio Orvieto , Adamos Solomou

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

Optimization and Control · Mathematics 2016-08-26 Zeyuan Allen-Zhu , Elad Hazan

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

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…

Machine Learning · Computer Science 2024-01-19 Jie Hao , Xiaochuan Gong , Mingrui Liu

We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…

Optimization and Control · Mathematics 2025-06-27 El Mahdi Chayti , Nikita Doikov , Martin Jaggi

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

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

Optimization and Control · Mathematics 2024-11-05 Pengyu Chen , Xu Shi , Rujun Jiang , Jiulin Wang

This paper explores second-order optimization methods in Federated Learning (FL), addressing the critical challenges of slow convergence and the excessive communication rounds required to achieve optimal performance from the global model.…

Machine Learning · Computer Science 2025-05-30 Mrinmay Sen , Sidhant R Nair , C Krishna Mohan

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

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

Optimization and Control · Mathematics 2016-07-15 Vahan Hovhannisyan , Panos Parpas , Stefanos Zafeiriou

Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…

Optimization and Control · Mathematics 2025-10-13 Hantao Nie , Jiaxiang Li , Zaiwen Wen