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We consider a distributed convex optimization problem in a network which is time-varying and not always strongly connected. The local cost function of each node is affected by some stochastic process. All nodes of the network collaborate to…

Optimization and Control · Mathematics 2021-05-27 Wenjie Li , Mohamad Assaad

This paper addresses stochastic optimization of Lipschitz-continuous, nonsmooth and nonconvex objectives over compact convex sets, where only noisy function evaluations are available. While gradient-free methods have been developed for…

Optimization and Control · Mathematics 2025-08-26 Anik Kumar Paul , Shalabh Bhatnagar

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

Optimization and Control · Mathematics 2018-11-13 Aryan Mokhtari , Hamed Hassani , Amin Karbasi

We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is…

Optimization and Control · Mathematics 2020-09-22 Eduard Gorbunov , Pavel Dvurechensky , Alexander Gasnikov

We study the complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order…

Optimization and Control · Mathematics 2024-04-16 Guy Kornowski , Ohad Shamir

Gradient clipping is a widely used technique in Machine Learning and Deep Learning (DL), known for its effectiveness in mitigating the impact of heavy-tailed noise, which frequently arises in the training of large language models.…

Optimization and Control · Mathematics 2025-09-30 Savelii Chezhegov , Aleksandr Beznosikov , Samuel Horváth , Eduard Gorbunov

Iterative optimization is central to modern artificial intelligence (AI) and provides a crucial framework for understanding adaptive systems. This review provides a unified perspective on this subject, bridging classic theory with neural…

Machine Learning · Computer Science 2025-10-22 Jesús García Fernández , Nasir Ahmad , Marcel van Gerven

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

In this letter, we first propose a \underline{Z}eroth-\underline{O}rder c\underline{O}ordinate \underline{M}ethod~(ZOOM) to solve the stochastic optimization problem over a decentralized network with only zeroth-order~(ZO) oracle feedback…

Optimization and Control · Mathematics 2022-10-11 Shengjun Zhang , Tan Shen , Hongwei Sun , Yunlong Dong , Dong Xie , Heng Zhang

In this work we address the problem of convex optimization in a multi-agent setting where the objective is to minimize the mean of local cost functions whose derivatives are not available (e.g. black-box models). Moreover agents can only…

Optimization and Control · Mathematics 2023-06-14 Alessio Maritan , Luca Schenato

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

Zeroth-order methods have become important tools for solving problems where we have access only to function evaluations. However, the zeroth-order methods only using gradient approximations are $n$ times slower than classical first-order…

Optimization and Control · Mathematics 2022-02-10 Erik Berglund , Sarit Khirirat , Xiaoyu Wang

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

Statistics Theory · Mathematics 2023-05-11 Yinan Shen , Jingyang Li , Jian-Feng Cai , Dong Xia

Fine-tuning large language models (LLMs) using zeroth-order (ZO) optimization has emerged as a promising alternative to traditional gradient-based methods due to its reduced memory footprint requirement. However, existing ZO methods suffer…

Machine Learning · Computer Science 2025-10-22 Zhendong Mi , Qitao Tan , Grace Li Zhang , Zhaozhuo Xu , Geng Yuan , Shaoyi Huang

Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging…

Optimization and Control · Mathematics 2021-02-23 Hongjian Wang , Mert Gürbüzbalaban , Lingjiong Zhu , Umut Şimşekli , Murat A. Erdogdu

Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…

Optimization and Control · Mathematics 2021-04-26 Guannan Liang , Qianqian Tong , Chunjiang Zhu , Jinbo Bi

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…

Optimization and Control · Mathematics 2015-10-27 Saeed Ghadimi , Guanghui Lan

Stochastic first-order methods such as Stochastic Extragradient (SEG) or Stochastic Gradient Descent-Ascent (SGDA) for solving smooth minimax problems and, more generally, variational inequality problems (VIP) have been gaining a lot of…

Optimization and Control · Mathematics 2022-11-02 Eduard Gorbunov , Marina Danilova , David Dobre , Pavel Dvurechensky , Alexander Gasnikov , Gauthier Gidel

This paper considers zeroth-order optimization for stochastic convex minimization problem. We propose a parameter-free stochastic zeroth-order method (POEM) by introducing a step-size scheme based on the distance over finite difference and…

Optimization and Control · Mathematics 2025-05-06 Kunjie Ren , Luo Luo