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In this paper, we determine the optimal convergence rates for strongly convex and smooth distributed optimization in two settings: centralized and decentralized communications over a network. For centralized (i.e. master/slave) algorithms,…

Optimization and Control · Mathematics 2017-04-10 Kevin Scaman , Francis Bach , Sébastien Bubeck , Yin Tat Lee , Laurent Massoulié

We consider the problem of decentralized optimization in networks with communication delays. To accommodate delays, we need decentralized optimization algorithms that work on directed graphs. Existing approaches require nodes to know their…

Optimization and Control · Mathematics 2024-12-31 Tomas Ortega , Hamid Jafarkhani

We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or…

Optimization and Control · Mathematics 2023-12-12 Dmitry Metelev , Aleksandr Beznosikov , Alexander Rogozin , Alexander Gasnikov , Anton Proskurnikov

We consider a distributed stochastic optimization problem that is solved by a decentralized network of agents with only local communication between neighboring agents. The goal of the whole system is to minimize a global objective function…

Optimization and Control · Mathematics 2022-11-10 Alexander Rogozin , Mikhail Bochko , Pavel Dvurechensky , Alexander Gasnikov , Vladislav Lukoshkin

In decentralized optimization, nodes of a communication network each possess a local objective function, and communicate using gossip-based methods in order to minimize the average of these per-node functions. While synchronous algorithms…

Optimization and Control · Mathematics 2022-09-02 Mathieu Even , Hadrien Hendrikx , Laurent Massoulie

We study decentralized asynchronous multiagent optimization over networks, modeled as static (possibly directed) graphs. The optimization problem consists of minimizing a (possibly nonconvex) smooth function--the sum of the agents' local…

Optimization and Control · Mathematics 2020-02-03 Ye Tian , Ying Sun , Gesualdo Scutari

We study the problem of decentralized optimization over time-varying networks with strongly convex smooth cost functions. In our approach, nodes run a multi-step gossip procedure after making each gradient update, thus ensuring approximate…

Optimization and Control · Mathematics 2022-11-08 Alexander Rogozin , Vladislav Lukoshkin , Alexander Gasnikov , Dmitry Kovalev , Egor Shulgin

We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over $n$ machines that can only communicate to their neighbors on a fixed communication graph. To…

Machine Learning · Computer Science 2019-02-04 Anastasia Koloskova , Sebastian U. Stich , Martin Jaggi

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

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

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

Decentralized optimization is emerging as a viable alternative for scalable distributed machine learning, but also introduces new challenges in terms of synchronization costs. To this end, several communication-reduction techniques, such as…

Machine Learning · Computer Science 2022-03-28 Giorgi Nadiradze , Amirmojtaba Sabour , Peter Davies , Shigang Li , Dan Alistarh

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…

Optimization and Control · Mathematics 2020-11-16 Dmitry Kovalev , Adil Salim , Peter Richtárik

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of $L$-smooth and $\mu$-strongly convex functions distributed over a given network of size $n$. Our key insight…

Optimization and Control · Mathematics 2023-12-07 Adel Nabli , Edouard Oyallon

In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing…

Machine Learning · Statistics 2019-01-25 Igor Colin , Aurélien Bellet , Joseph Salmon , Stéphan Clémençon

We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the…

Optimization and Control · Mathematics 2023-01-30 Dmitriy Metelev , Alexander Rogozin , Dmitry Kovalev , Alexander Gasnikov

This paper considers the minimization of a sum of smooth and strongly convex functions dispatched over the nodes of a communication network. Previous works on the subject either focus on synchronous algorithms, which can be heavily slowed…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-09 Mathieu Even , Hadrien Hendrikx , Laurent Massoulié

Decentralized learning on resource-constrained edge devices demands algorithms that are communication-efficient, robust to data corruption, and lightweight in memory. State-of-the-art gossip-based methods address communication efficiency,…

Machine Learning · Computer Science 2026-05-08 Anna van Elst , Igor Colin , Stephan Clémençon

Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence…

Machine Learning · Computer Science 2021-03-03 Anastasia Koloskova , Nicolas Loizou , Sadra Boreiri , Martin Jaggi , Sebastian U. Stich

We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…

Optimization and Control · Mathematics 2024-05-29 Dmitry Kovalev , Ekaterina Borodich , Alexander Gasnikov , Dmitrii Feoktistov
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