An Exact Quantized Decentralized Gradient Descent Algorithm

We consider the problem of decentralized consensus optimization, where the sum of <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> smooth and strongly convex functions are minimized over <inline-formula><tex-math notation="LaTeX...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 67; no. 19; pp. 4934 - 4947
Main Authors: Reisizadeh, Amirhossein, Mokhtari, Aryan, Hassani, Hamed, Pedarsani, Ramtin
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Communication-efficiency
Computer simulation
Convergence
Convex functions
Convexity
Counters
decentralized optimization
gradient methods
Linear programming
Nickel
Nodes
Optimization
quantization
Quantization (signal)
Signal processing algorithms
Smoothness
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:We consider the problem of decentralized consensus optimization, where the sum of <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> smooth and strongly convex functions are minimized over <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local information. We prove that under standard strong convexity and smoothness assumptions for the objective function, QDGD achieves a vanishing mean solution error under customary conditions for quantizers. To the best of our knowledge, this is the first algorithm that achieves vanishing consensus error in the presence of quantization noise. Moreover, we provide simulation results that show tight agreement between our derived theoretical convergence rate and the numerical results.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2932876