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One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms,…

Optimization and Control · Mathematics 2016-05-24 Conghui Tan , Shiqian Ma , Yu-Hong Dai , Yuqiu Qian

Federated Learning (FL) enables multiple clients to collaboratively train models without sharing raw data, but is vulnerable to Byzantine attacks and data heterogeneity, which can severely degrade performance. Existing Byzantine-robust…

Machine Learning · Computer Science 2025-10-28 Shiyuan Zuo , Xingrun Yan , Rongfei Fan , Li Shen , Puning Zhao , Jie Xu , Han Hu

In this paper, we propose BR-MTRL, a Byzantine-resilient multi-task representation learning framework that handles faulty or malicious agents. Our approach leverages representation learning through a shared neural network model, where all…

Machine Learning · Computer Science 2025-11-03 Tuan Le , Shana Moothedath

We give a sharp convergence rate for the asynchronous stochastic gradient descent (ASGD) algorithms when the loss function is a perturbed quadratic function based on the stochastic modified equations introduced in [An et al. Stochastic…

Numerical Analysis · Mathematics 2020-01-27 Yuhua Zhu , Lexing Ying

As the size of models and datasets grows, it has become increasingly common to train models in parallel. However, existing distributed stochastic gradient descent (SGD) algorithms suffer from insufficient utilization of computational…

Machine Learning · Computer Science 2023-08-30 Xin Zhou , Ling Chen , Houming Wu

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

Machine Learning · Statistics 2023-06-23 Gerard Ben Arous , Reza Gheissari , Aukosh Jagannath

In distributed learning, sign-based compression algorithms such as signSGD with majority vote provide a lightweight alternative to SGD with an additional advantage: fault tolerance (almost) for free. However, for signSGD with majority vote,…

Machine Learning · Computer Science 2025-03-12 Emanuele Mengoli , Luzius Moll , Virgilio Strozzi , El-Mahdi El-Mhamdi

We consider gradient coding in the presence of an adversary, controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the inputs of the malicious workers as errors and…

Information Theory · Computer Science 2023-06-06 Christoph Hofmeister , Luis Maßny , Eitan Yaakobi , Rawad Bitar

We consider the problem of Byzantine fault-tolerance in the peer-to-peer (P2P) distributed gradient-descent method -- a prominent algorithm for distributed optimization in a P2P system. In this problem, the system comprises of multiple…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-01 Nirupam Gupta , Nitin H. Vaidya

We investigate robust federated learning, where a group of workers collaboratively train a shared model under the orchestration of a central server in the presence of Byzantine adversaries capable of arbitrary and potentially malicious…

Machine Learning · Computer Science 2025-11-05 Lihan Xu , Yanjie Dong , Gang Wang , Runhao Zeng , Xiaoyi Fan , Xiping Hu

The BG-simulation is a powerful reduction algorithm designed for asynchronous read/write crash-prone systems. It allows a set of $(t+1)$ asynchronous sequential processes to wait-free simulate (i.e., despite the crash of up to $t$ of them)…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-07-15 Damien Imbs , Michel Raynal , Julien Stainer

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Machine Learning · Computer Science 2024-02-13 Anuraganand Sharma

This paper develops an efficient distributed inference algorithm, which is robust against a moderate fraction of Byzantine nodes, namely arbitrary and possibly adversarial machines in a distributed learning system. In robust statistics, the…

Machine Learning · Statistics 2021-03-05 Jiyuan Tu , Weidong Liu , Xiaojun Mao , Xi Chen

Federated learning has arisen as a mechanism to allow multiple participants to collaboratively train a model without sharing their data. In these settings, participants (workers) may not trust each other fully; for instance, a set of…

Machine Learning · Computer Science 2021-07-28 Kamala Varma , Yi Zhou , Nathalie Baracaldo , Ali Anwar

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Optimization and Control · Mathematics 2019-04-30 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

Machine Learning · Computer Science 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…

Machine Learning · Computer Science 2020-03-30 Naeimeh Omidvar , Mohammad Ali Maddah-Ali , Hamed Mahdavi

We revisit Byzantine robust distributed estimation for high-dimensional sparse linear models. By combining local $\ell_1$-regularized robust estimation with robust aggregation at the server, the framework applies to pseudo-Huber regression,…

Machine Learning · Computer Science 2026-05-14 Yuxuan Wang , Lixin Zhang , Kangqiang Li

Federated Learning (FL) emerges as a distributed machine learning approach that addresses privacy concerns by training AI models locally on devices. Decentralized Federated Learning (DFL) extends the FL paradigm by eliminating the central…

Machine Learning · Computer Science 2025-11-17 Diego Cajaraville-Aboy , Ana Fernández-Vilas , Rebeca P. Díaz-Redondo , Manuel Fernández-Veiga

Most existing Byzantine-robust federated learning (FL) methods suffer from slow and unstable convergence. Moreover, when handling a substantial proportion of colluded malicious clients, achieving robustness typically entails compromising…

Machine Learning · Computer Science 2026-04-17 He Yang , Dongyi Lv , Wei Xi , Song Ma , Hanlin Gu , Jizhong Zhao