Random Walk Gradient Descent for Decentralized Learning on Graphs

We consider a decentralized learning setting in which data is distributed over nodes in a graph.The goal is to learn a global model on the distributed data without involving any central entity that needs to be trusted. While gossip-based stochastic gradient descent (SGD) can be used to achieve this learning objective, it incurs high communication and computation costs, since it has to wait for all the local models at all the nodes to converge. To speed up the convergence, we propose instead to study random walk based SGD in which a global model is updated based on a random walk on the graph.We propose two algorithms based on two types of random walks that achieve, in a decentralized way, uniform sampling and importance sampling of the data. We provide a non-asymptotic analysis on the rate of convergence, taking into account the constants related to the data and the graph. Our numerical results show that the weighted random walk based algorithm has a better performance for high-variance data. Moreover, we propose a privacy-preserving random walk algorithm that achieves local differential privacy based on a Gamma noise mechanism that we propose. We also give numerical results on the convergence of this algorithm and show that it outperforms additive Laplace-based privacy mechanisms.

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“…Parts of these results pertaining to Algorithms 1 and 2 have already appeared in a conference paper [20].…”

Section: Moreover We Propose a Privacy-preserving Version Of Them Bas...mentioning

confidence: 95%

Private Weighted Random Walk Stochastic Gradient Descent

Ayache

Rouayheb

2021

IEEE J. Sel. Areas Inf. Theory

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“…2) Otherwise, if the candidate node gets rejected, the random walk stays at the same node, i.e., i (k+1) = i (k) . b) Static Weighted Random Walk: This algorithm assigns a static importance metric to each node that is proportional to the gradient-Lipschitz constant of the local loss function [42], [50]. The random walk is designed by the MH again with a stationary distribution that is proportional to the local gradient-Lipschitz constants.…”

Section: A Baseline Algorithmsmentioning

confidence: 99%

Walk for Learning: A Random Walk Approach for Federated Learning from Heterogeneous Data

Ayache¹,

Dassari²,

Rouayheb³

2022

Preprint

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We consider the problem of a Parameter Server (PS) that wishes to learn a model that fits data distributed on the nodes of a graph. We focus on Federated Learning (FL) as a canonical application. One of the main challenges of FL is the communication bottleneck between the nodes and the parameter server. A popular solution in the literature is to allow each node to do several local updates on the model in each iteration before sending it back to the PS. While this mitigates the communication bottleneck, the statistical heterogeneity of the data owned by the different nodes has proven to delay convergence and bias the model.In this work, we study random walk (RW) learning algorithms for tackling the communication and data heterogeneity problems. The main idea is to leverage available direct connections among the nodes themselves, which are typically "cheaper" than the communication to the PS. In a random walk, the model is thought of as a "baton" that is passed from a node to one of its neighbors after being updated in each iteration.The challenge in designing the RW is the data heterogeneity and the uncertainty about the data distributions. Ideally, we would want to visit more often nodes that hold more informative data. We cast this problem as a sleeping multiarmed bandit (MAB) to design near-optimal node sampling strategy that achieves a variance reduced gradient estimates and approaches sub-linearly the optimal sampling strategy. Based on this framework, we present an adaptive random walk learning algorithm. We provide theoretical guarantees on its convergence. Our numerical results validate our theoretical findings and show that our algorithm outperforms existing random walk algorithms.

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