# Decentralized Asynchronous Non-convex Stochastic Optimization on Directed Graphs

Source: [Decentralized Asynchronous Non-convex Stochastic Optimization on Directed Graphs](<https://www.sota2.com/research/paper/68fa588f1e209131ce9af5bc>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T05:19:44.543Z

Authors: Vyacheslav Kungurtsev, Mahdi Morafah, Tara Javidi, Gesualdo Scutari

Published: 2021-10-20T06:56:42.000Z

## Abstract

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 a collective (additive) objective function consisting of agents' individual (possibly non-convex) local objective functions. Each agent only has access to a noisy estimate of the gradient of its own function (one component of the sum of objective functions). We proposed an asynchronous distributed algorithm for such a class of problems. The algorithm combines stochastic gradients with tracking in an asynchronous push-sum framework and obtain the standard sublinear convergence rate for general non-convex functions, matching the rate of centralized stochastic gradient descent SGD.   Our experiments on a non-convex image classification task using convolutional neural network validate the convergence of our proposed algorithm across different number of nodes and graph connectivity percentages.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2110.10406>)

[PDF](<https://arxiv.org/pdf/2110.10406.pdf>)