Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs

Nedić, Angelia; Olshevsky, Alex

doi:10.1109/tac.2016.2529285

Cited by 267 publications

(198 citation statements)

References 37 publications

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“…In addition, a dual subgradient averaging method is proposed for solving the same problem, which is shown to have better convergence results in terms of network scaling [10]. Some extension has also been made for cases under constraints [11], [12], cases where only noisy gradient is available [13], [14] and directed graphs [15]. A common issue of the abovementioned method is that they require decaying stepsize and the assumption of bounded (sub)gradient to achieve the exact optimum.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed distributed algorithm allows for using uncoordinated stepsizes for local optimization and, in contrast to most existing literatures, is guaranteed to converge to the exact optimum even with constant stepsizes. Note that our assumption is similar with [7] and [14] except for that we drop the strongly convex assumption but it is quite different from most (sub)gradient-based methods [9], [25], [26] where the (sub)gradients are usually assumed to be bounded, which is quite restrictive in unconstrained optimization problems. It is also important to note that our approach, though, has similar form with the ones proposed in [23], [26]- [28], it differs from them in its nature in that our assumptions (c.f.…”

Section: Introductionmentioning

confidence: 99%

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Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes

Zhu

Soh

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

269

293

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We consider distributed optimization problems in which a number of agents are to seek the optimum of a global objective function through merely local information sharing. The problem arises in various application domains, such as resource allocation, sensor fusion and distributed learning. In particular, we are interested in scenarios where agents use uncoordinated (different) constant stepsizes for local optimization. According to most existing works, using this kind of stepsize rule for update, which is necessary in asynchronous scenarios, will lead to some gap (error) between the estimated result and the exact optimum. To deal with this issue, we develop a new augmented distributed gradient method (termed Aug-DGM) based on consensus theory. The proposed algorithm not only allows for using uncoordinated stepsizes but also, most importantly, be able to seek the exact optimum even with constant stepsizes assuming that the global objective function has Lipschitz gradient. A simple numerical example is provided to illustrate the effectiveness of the algorithm.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes

Zhu

Soh

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

269

293

View full text Add to dashboard Cite

show abstract

“…We note that more involved gossip protocols have been proposed, we mention for instance broad-cast and push-sum protocols (see [29] and [30]). Although theoretically possible, such an extension of Algorithm 3 is however beyond the scope of this paper.…”

Section: Algorithm 3: Distributed On-line Mle (Domle)mentioning

confidence: 99%

Distributed on-line multidimensional scaling for self-localization in wireless sensor networks

Morral

Bianchi

2016

Signal Processing

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The present work considers the localization problem in wireless sensor networks formed by fixed nodes. Each node seeks to estimate its own position based on noisy measurements of the relative distance to other nodes. In a centralized batch mode, positions can be retrieved (up to a rigid transformation) by applying Principal Component Analysis (PCA) on a so-called similarity matrix built from the relative distances. In this paper, we propose a distributed on-line algorithm allowing each node to estimate its own position based on limited exchange of information in the network. Our framework encompasses the case of sporadic measurements and random link failures. We prove the consistency of our algorithm in the case of fixed sensors. Finally, we provide numerical and experimental results from both simulated and real data. Simulations issued to real data are conducted on a wireless sensor network testbed.

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“…Distributed algorithms for solving stochastic problems have been widely studied [6][7][8][9][10][11]. On the other side, distributed algorithms for big-data problems through block communication have started to appear only recently [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

On the Linear Convergence Rate of the Distributed Block Proximal Method

Farina

Notarstefano

2020

IEEE Control Syst. Lett.

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The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local objective functions. This class of problems arises in many learning and classification problems in which, for example, strongly-convex regularizing functions are included in the objective function, the decision variable is extremely high dimensional, and large datasets are employed. The algorithm produces local estimates by means of block-wise updates and communication among the agents. The expected distance from the (global) optimum, in terms of cost value, is shown to decay linearly to a constant value which is proportional to the selected local stepsizes. A numerical example involving a classification problem corroborates the theoretical results. * This result is part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 638992 -OPT4SMART). c 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs

Cited by 267 publications

References 37 publications

Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes

Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes

Distributed on-line multidimensional scaling for self-localization in wireless sensor networks

On the Linear Convergence Rate of the Distributed Block Proximal Method

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