Finite-Bit Quantization for Distributed Algorithms With Linear Convergence
This paper studies distributed algorithms for (strongly convex) composite optimization problems over mesh networks, subject to quantized communications. Instead of focusing on a specific algorithmic design, a black-box model is proposed, casting linearly convergent distributed algorithms in the form...
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| Vydáno v: | IEEE transactions on information theory Ročník 68; číslo 11; s. 7254 - 7280 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.11.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | This paper studies distributed algorithms for (strongly convex) composite optimization problems over mesh networks, subject to quantized communications. Instead of focusing on a specific algorithmic design, a black-box model is proposed, casting linearly convergent distributed algorithms in the form of fixed-point iterates. The algorithmic model is equipped with a novel random or deterministic Biased Compression (BC) rule on the quantizer design, and a new Adaptive encoding Non-uniform Quantizer (ANQ) coupled with a communication-efficient encoding scheme, which implements the BC-rule using a finite number of bits (below machine precision). This fills a gap existing in most state-of-the-art quantization schemes, such as those based on the popular compression rule, which rely on communication of some scalar signals with negligible quantization error (in practice quantized at the machine precision). A unified communication complexity analysis is developed for the black-box model, determining the average number of bits required to reach a solution of the optimization problem within a target accuracy. It is shown that the proposed BC-rule preserves linear convergence of the unquantized algorithms, and a trade-off between convergence rate and communication cost under ANQ-based quantization is characterized. Numerical results validate our theoretical findings and show that distributed algorithms equipped with the proposed ANQ have more favorable communication cost than algorithms using state-of-the-art quantization rules. |
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| AbstractList | This paper studies distributed algorithms for (strongly convex) composite optimization problems over mesh networks, subject to quantized communications. Instead of focusing on a specific algorithmic design, a black-box model is proposed, casting linearly convergent distributed algorithms in the form of fixed-point iterates. The algorithmic model is equipped with a novel random or deterministic Biased Compression (BC) rule on the quantizer design, and a new Adaptive encoding Non-uniform Quantizer (ANQ) coupled with a communication-efficient encoding scheme, which implements the BC-rule using a finite number of bits (below machine precision). This fills a gap existing in most state-of-the-art quantization schemes, such as those based on the popular compression rule, which rely on communication of some scalar signals with negligible quantization error (in practice quantized at the machine precision). A unified communication complexity analysis is developed for the black-box model, determining the average number of bits required to reach a solution of the optimization problem within a target accuracy. It is shown that the proposed BC-rule preserves linear convergence of the unquantized algorithms, and a trade-off between convergence rate and communication cost under ANQ-based quantization is characterized. Numerical results validate our theoretical findings and show that distributed algorithms equipped with the proposed ANQ have more favorable communication cost than algorithms using state-of-the-art quantization rules. |
| Author | Scutari, Gesualdo Lee, Chang-Shen Michelusi, Nicolo |
| Author_xml | – sequence: 1 givenname: Nicolo orcidid: 0000-0002-5521-6496 surname: Michelusi fullname: Michelusi, Nicolo email: nicolo.michelusi@asu.edu organization: School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, USA – sequence: 2 givenname: Gesualdo orcidid: 0000-0002-6453-6870 surname: Scutari fullname: Scutari, Gesualdo email: gscutari@purdue.edu organization: School of Industrial Engineering, Purdue University, West Lafayette, IN, USA – sequence: 3 givenname: Chang-Shen orcidid: 0000-0002-1982-7011 surname: Lee fullname: Lee, Chang-Shen email: ben3003neb@gmail.com organization: Bloomberg, New York City, NY, USA |
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| SubjectTerms | Algorithms Communication Convergence Costs Distributed algorithms Finite element method linear convergence Mathematical models Measurement Mesh networks Optimization optimization methods quantization Quantization (signal) Stars |
| Title | Finite-Bit Quantization for Distributed Algorithms With Linear Convergence |
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