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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| Published in: | IEEE transactions on signal processing Vol. 67; no. 19; pp. 4934 - 4947 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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IEEE
01.10.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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| Abstract | 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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| AbstractList | We consider the problem of decentralized consensus optimization, where the sum of [Formula Omitted] smooth and strongly convex functions are minimized over [Formula Omitted] 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. 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. |
| Author | Pedarsani, Ramtin Reisizadeh, Amirhossein Hassani, Hamed Mokhtari, Aryan |
| Author_xml | – sequence: 1 givenname: Amirhossein orcidid: 0000-0002-1730-8402 surname: Reisizadeh fullname: Reisizadeh, Amirhossein email: reisizadeh@ucsb.edu organization: Department of Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA – sequence: 2 givenname: Aryan surname: Mokhtari fullname: Mokhtari, Aryan email: mokhtari@austin.utexas.edu organization: Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA – sequence: 3 givenname: Hamed surname: Hassani fullname: Hassani, Hamed email: hassani@seas.upenn.edu organization: Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA – sequence: 4 givenname: Ramtin orcidid: 0000-0002-1126-0292 surname: Pedarsani fullname: Pedarsani, Ramtin email: ramtin@ece.ucsb.edu organization: Department of Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA |
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| SubjectTerms | 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 |
| Title | An Exact Quantized Decentralized Gradient Descent Algorithm |
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