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The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…

Optimization and Control · Mathematics 2024-03-13 Anastasia Borovykh , Nikolas Kantas , Panos Parpas , Grigorios A. Pavliotis

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…

Optimization and Control · Mathematics 2018-08-23 Deming Yuan , Yiguang Hong , Daniel W. C. Ho , Guoping Jiang

We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network…

Machine Learning · Statistics 2018-04-03 Ahmed Zaki , Saikat Chatterjee , Partha P. Mitra , Lars K. Rasmussen

We study distributed stochastic convex optimization under the delayed gradient model where the server nodes perform parameter updates, while the worker nodes compute stochastic gradients. We discuss, analyze, and experiment with a setup…

Machine Learning · Statistics 2015-08-21 Suvrit Sra , Adams Wei Yu , Mu Li , Alexander J. Smola

This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively…

Optimization and Control · Mathematics 2025-08-14 Wentao Zhang , Baoyong Zhang , Deming Yuan , Shengyuan Xu , Vincent K. N. Lau

Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…

Machine Learning · Statistics 2018-10-30 Ashok Cutkosky , Robert Busa-Fekete

We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired…

Optimization and Control · Mathematics 2022-04-19 Mohammad Taha Toghani , César A. Uribe

Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly…

Optimization and Control · Mathematics 2022-10-12 Changxin Liu , Zirui Zhou , Jian Pei , Yong Zhang , Yang Shi

Big data, including applications with high security requirements, are often collected and stored on multiple heterogeneous devices, such as mobile devices, drones and vehicles. Due to the limitations of communication costs and security…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-10-05 Hao Chen , Yu Ye , Ming Xiao , Mikael Skoglund , H. Vincent Poor

We consider the problem of decentralized optimization over time-varying directed networks. The network nodes can access only their local objectives, and aim to collaboratively minimize a global function by exchanging messages with their…

Systems and Control · Electrical Eng. & Systems 2021-12-03 Yiyue Chen , Abolfazl Hashemi , Haris Vikalo

We consider distributed optimization by a collection of nodes, each having access to its own convex function, whose collective goal is to minimize the sum of the functions. The communications between nodes are described by a time-varying…

Optimization and Control · Mathematics 2014-03-18 Angelia Nedic , Alex Olshevsky

Decentralized learning algorithms empower interconnected devices to share data and computational resources to collaboratively train a machine learning model without the aid of a central coordinator. In the case of heterogeneous data…

Machine Learning · Computer Science 2023-01-16 Matteo Zecchin , Marios Kountouris , David Gesbert

Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform…

Optimization and Control · Mathematics 2020-11-06 Haoran Sun , Songtao Lu , Mingyi Hong

The paper considers distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents' local expectation-valued convex cost functions. Due to the stochasticity in gradient…

Optimization and Control · Mathematics 2022-04-07 Jinlong Lei , Peng Yi , Jie Chen , Yiguang Hong

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 propose a distributed algorithm, called Directed-Distributed Gradient Descent (D-DGD), to solve multi-agent optimization problems over directed graphs. Existing algorithms mostly deal with similar problems under the…

Optimization and Control · Mathematics 2016-02-02 Chenguang Xi , Qiong Wu , Usman A. Khan

In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…

Optimization and Control · Mathematics 2026-04-14 Yeong-Ung Kim , Hyo-Sung Ahn

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced…

Optimization and Control · Mathematics 2020-05-22 Hadrien Hendrikx , Francis Bach , Laurent Massoulie

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

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced…

Optimization and Control · Mathematics 2019-06-13 Hadrien Hendrikx , Francis Bach , Laurent Massoulie