Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions

Igor Colin, Aurelien Bellet, Joseph Salmon, Stéphan Clémençon
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1388-1396, 2016.

Abstract

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 unit. In this paper, we address the problem of decentralized minimization of pairwise functions of the data points, where these points are distributed over the nodes of a graph defining the communication topology of the network. This general problem finds applications in ranking, distance metric learning and graph inference, among others. We propose new gossip algorithms based on dual averaging which aims at solving such problems both in synchronous and asynchronous settings. The proposed framework is flexible enough to deal with constrained and regularized variants of the optimization problem. Our theoretical analysis reveals that the proposed algorithms preserve the convergence rate of centralized dual averaging up to an additive bias term. We present numerical simulations on Area Under the ROC Curve (AUC) maximization and metric learning problems which illustrate the practical interest of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-colin16, title = {Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions}, author = {Colin, Igor and Bellet, Aurelien and Salmon, Joseph and Clémençon, Stéphan}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {1388--1396}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/colin16.pdf}, url = {https://proceedings.mlr.press/v48/colin16.html}, abstract = {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 unit. In this paper, we address the problem of decentralized minimization of pairwise functions of the data points, where these points are distributed over the nodes of a graph defining the communication topology of the network. This general problem finds applications in ranking, distance metric learning and graph inference, among others. We propose new gossip algorithms based on dual averaging which aims at solving such problems both in synchronous and asynchronous settings. The proposed framework is flexible enough to deal with constrained and regularized variants of the optimization problem. Our theoretical analysis reveals that the proposed algorithms preserve the convergence rate of centralized dual averaging up to an additive bias term. We present numerical simulations on Area Under the ROC Curve (AUC) maximization and metric learning problems which illustrate the practical interest of our approach.} }
Endnote
%0 Conference Paper %T Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions %A Igor Colin %A Aurelien Bellet %A Joseph Salmon %A Stéphan Clémençon %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-colin16 %I PMLR %P 1388--1396 %U https://proceedings.mlr.press/v48/colin16.html %V 48 %X 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 unit. In this paper, we address the problem of decentralized minimization of pairwise functions of the data points, where these points are distributed over the nodes of a graph defining the communication topology of the network. This general problem finds applications in ranking, distance metric learning and graph inference, among others. We propose new gossip algorithms based on dual averaging which aims at solving such problems both in synchronous and asynchronous settings. The proposed framework is flexible enough to deal with constrained and regularized variants of the optimization problem. Our theoretical analysis reveals that the proposed algorithms preserve the convergence rate of centralized dual averaging up to an additive bias term. We present numerical simulations on Area Under the ROC Curve (AUC) maximization and metric learning problems which illustrate the practical interest of our approach.
RIS
TY - CPAPER TI - Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions AU - Igor Colin AU - Aurelien Bellet AU - Joseph Salmon AU - Stéphan Clémençon BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-colin16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 1388 EP - 1396 L1 - http://proceedings.mlr.press/v48/colin16.pdf UR - https://proceedings.mlr.press/v48/colin16.html AB - 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 unit. In this paper, we address the problem of decentralized minimization of pairwise functions of the data points, where these points are distributed over the nodes of a graph defining the communication topology of the network. This general problem finds applications in ranking, distance metric learning and graph inference, among others. We propose new gossip algorithms based on dual averaging which aims at solving such problems both in synchronous and asynchronous settings. The proposed framework is flexible enough to deal with constrained and regularized variants of the optimization problem. Our theoretical analysis reveals that the proposed algorithms preserve the convergence rate of centralized dual averaging up to an additive bias term. We present numerical simulations on Area Under the ROC Curve (AUC) maximization and metric learning problems which illustrate the practical interest of our approach. ER -
APA
Colin, I., Bellet, A., Salmon, J. & Clémençon, S.. (2016). Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:1388-1396 Available from https://proceedings.mlr.press/v48/colin16.html.

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