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We study high-probability convergence in online learning, in the presence of heavy-tailed noise. To combat the heavy tails, a general framework of nonlinear SGD methods is considered, subsuming several popular nonlinearities like sign,…

Machine Learning · Computer Science 2025-03-24 Aleksandar Armacki , Shuhua Yu , Pranay Sharma , Gauri Joshi , Dragana Bajovic , Dusan Jakovetic , Soummya Kar

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

Optimization and Control · Mathematics 2019-05-15 Michael R. Metel , Akiko Takeda

Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…

Statistics Theory · Mathematics 2023-05-12 Yinan Shen , Jingyang Li , Jian-Feng Cai , Dong Xia

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

Optimization and Control · Mathematics 2019-05-17 Radu Ioan Bot , Axel Böhm

This paper investigates the distributed continuous-time nonconvex optimization problem over unbalanced directed networks. The objective is to cooperatively drive all the agent states to an optimal solution that minimizes the sum of the…

Optimization and Control · Mathematics 2022-12-01 Jin Zhang , Yahui Hao , Lu Liu , Haibo Ji

The success of deep learning depends on large-scale and well-curated training data, while data in real-world applications are commonly long-tailed and noisy. Many methods have been proposed to deal with long-tailed data or noisy data, while…

Machine Learning · Computer Science 2023-05-30 Lefan Zhang , Zhang-Hao Tian , Wujun Zhou , Wei Wang

Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…

Machine Learning · Computer Science 2025-10-27 Xingyu Wang , Chang-Han Rhee

We consider stochastic optimization with delayed gradients where, at each time step $t$, the algorithm makes an update using a stale stochastic gradient from step $t - d_t$ for some arbitrary delay $d_t$. This setting abstracts asynchronous…

Optimization and Control · Mathematics 2021-11-16 Alon Cohen , Amit Daniely , Yoel Drori , Tomer Koren , Mariano Schain

We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…

Statistics Theory · Mathematics 2019-07-08 Anatoli Juditsky , Alexander Nazin , Arkadi Nemirovsky , Alexandre Tsybakov

This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…

Optimization and Control · Mathematics 2024-04-01 Dongyu Han , Kun Liu , Yeming Lin , Yuanqing Xia

One of the most widely used methods for solving large-scale stochastic optimization problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent…

Optimization and Control · Mathematics 2021-07-08 Zhengyuan Zhou , Panayotis Mertikopoulos , Nicholas Bambos , Peter W. Glynn , Yinyu Ye

In this paper, we characterize the noise of stochastic gradients and analyze the noise-induced dynamics during training deep neural networks by gradient-based optimizers. Specifically, we firstly show that the stochastic gradient noise…

Machine Learning · Computer Science 2021-09-22 Yixin Wu , Rui Luo , Chen Zhang , Jun Wang , Yaodong Yang

An increasing number of studies have focused on stochastic first-order methods (SFOMs) under heavy-tailed gradient noises, which have been observed in the training of practical deep learning models. In this paper, we focus on two types of…

Optimization and Control · Mathematics 2025-07-18 Tianxi Zhu , Yi Xu , Xiangyang Ji

Distributed Optimization is an increasingly important subject area with the rise of multi-agent control and optimization. We consider a decentralized stochastic optimization problem where the agents on a graph aim to asynchronously optimize…

Optimization and Control · Mathematics 2021-10-22 Vyacheslav Kungurtsev , Mahdi Morafah , Tara Javidi , Gesualdo Scutari

We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…

Optimization and Control · Mathematics 2025-01-22 Damek Davis , Dmitriy Drusvyatskiy , Zhan Shi

This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…

Optimization and Control · Mathematics 2020-02-17 Jinlong Lei , Peng Yi , Jie Chen , Yiguang Hong

ADMM is a popular algorithm for solving convex optimization problems. Applying this algorithm to distributed consensus optimization problem results in a fully distributed iterative solution which relies on processing at the nodes and…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-01-17 Layla Majzoobi , Farshad Lahouti

Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…

Machine Learning · Computer Science 2020-12-01 Matthew Nokleby , Haroon Raja , Waheed U. Bajwa

We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed network of connections. We propose a…

Optimization and Control · Mathematics 2021-06-29 Arya Akhavan , Massimiliano Pontil , Alexandre B. Tsybakov

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

Methodology · Statistics 2019-03-12 Yuan Ke , Stanislav Minsker , Zhao Ren , Qiang Sun , Wen-Xin Zhou