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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Published in:	IEEE transactions on information theory Vol. 68; no. 11; pp. 7254 - 7280
Main Authors:	Michelusi, Nicolo, Scutari, Gesualdo, Lee, Chang-Shen
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.11.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Communication Convergence Costs Distributed algorithms Finite element method linear convergence Mathematical models Measurement Mesh networks Optimization optimization methods quantization Quantization (signal) Stars
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.
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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References	ref13 ref57 ref12 ref56 ref15 ref14 Alistarh (ref53) ref58 Zhang (ref39) 2021 ref11 ref10 ref17 ref16 ref19 ref18 ref51 Koloskova (ref6) ref50 ref46 ref45 ref48 ref47 Stich (ref29) ref42 ref41 ref44 Lian (ref5) ref43 ref49 Stich (ref35) 2020 ref8 ref7 ref9 Agarwal (ref55) ref4 ref3 Gorbunov (ref34) ref40 Taheri (ref36) ref31 Kovalev (ref24) Liao (ref38) 2021 ref2 Alistarh (ref27) ref1 Beznosikov (ref33) 2020 ref23 Liu (ref25) Bertsekas (ref52) 1989 ref20 ref22 Davies (ref54) ref21 Tang (ref30) Alistarh (ref26) Haddadpour (ref37) Karimireddy (ref28) Zheng (ref32)
References_xml	– ident: ref9 doi: 10.1109/TAC.2009.2031203 – volume-title: arXiv:2009.02388 year: 2020 ident: ref35 article-title: On communication compression for distributed optimization on heterogeneous data – start-page: 7254 volume-title: Proc. 35th NeurIPS ident: ref53 article-title: Towards tight communication lower bounds for distributed optimisation – ident: ref2 doi: 10.1007/978-3-319-97142-1 – volume-title: Parallel and Distributed Computation: Numerical Methods year: 1989 ident: ref52 – start-page: 1709 volume-title: Proc. 31st NeurIPS ident: ref26 article-title: QSGD: Communication-efficient SGD via gradient quantization and encoding – ident: ref20 doi: 10.1109/ACSSC.2018.8645345 – ident: ref49 doi: 10.1007/s10107-018-01357-w – ident: ref14 doi: 10.1109/TSP.2012.2223692 – ident: ref46 doi: 10.1109/TCNS.2017.2698261 – ident: ref40 doi: 10.1109/TSIPN.2016.2524588 – ident: ref7 doi: 10.1016/j.automatica.2007.01.002 – ident: ref17 doi: 10.1109/TNNLS.2016.2519894 – ident: ref13 doi: 10.1109/TAC.2011.2160593 – ident: ref21 doi: 10.1109/TAC.2020.2989281 – ident: ref42 doi: 10.1080/10556788.2020.1750013 – ident: ref3 doi: 10.1016/j.arcontrol.2019.05.006 – ident: ref16 doi: 10.1109/TAC.2016.2530939 – start-page: 3252 volume-title: Proc. 36th ICML ident: ref28 article-title: Error feedback fixes SignSGD and other gradient compression schemes – ident: ref47 doi: 10.1109/TAC.2008.2009515 – ident: ref23 doi: 10.1109/TAC.2020.3030871 – ident: ref57 doi: 10.1109/5.726791 – start-page: 7652 volume-title: Proc. 32nd NeurIPS ident: ref30 article-title: Communication compression for decentralized training – ident: ref58 doi: 10.24033/bsmf.1625 – ident: ref12 doi: 10.1109/TSP.2010.2077282 – ident: ref44 doi: 10.1109/TAC.2017.2730481 – start-page: 5973 volume-title: Proc. 32nd NeurIPS ident: ref27 article-title: The convergence of sparsified gradient methods – ident: ref11 doi: 10.1109/TAC.2010.2052384 – volume-title: arXiv:2105.06697 year: 2021 ident: ref39 article-title: Innovation compression for communication-efficient distributed optimization with linear convergence – ident: ref18 doi: 10.1109/ACSSC.2017.8335401 – ident: ref1 doi: 10.1109/TSG.2017.2720471 – start-page: 680 volume-title: Proc. 23rd AISTATS ident: ref34 article-title: A unified theory of SGD: Variance reduction, sampling, quantization and coordinate descent – volume-title: Proc. 9th ICLR ident: ref25 article-title: Linear convergent decentralized optimization with compression – ident: ref48 doi: 10.1109/TSP.2019.2926022 – ident: ref19 doi: 10.1109/CDC.2018.8618973 – ident: ref15 doi: 10.1109/TSP.2015.2441034 – ident: ref56 doi: 10.1016/j.sysconle.2004.02.022 – start-page: 4087 volume-title: Proc. 24th AISTATS ident: ref24 article-title: A linearly convergent algorithm for decentralized optimization: Sending less bits for free! – ident: ref50 doi: 10.1109/TSP.2021.3086579 – start-page: 3478 volume-title: Proc. 36th ICML ident: ref6 article-title: Decentralized stochastic optimization and gossip algorithms with compressed communication – ident: ref45 doi: 10.1137/16M1084316 – volume-title: arXiv:2002.12410 year: 2020 ident: ref33 article-title: On biased compression for distributed learning – start-page: 2350 volume-title: Proc. 24th AISTATS ident: ref37 article-title: Federated learning with compression: Unified analysis and sharp guarantees – ident: ref51 doi: 10.1007/978-1-4419-8853-9 – ident: ref43 doi: 10.1137/14096668X – start-page: 37 volume-title: Proc. 24th NeurIPS ident: ref55 article-title: Fast global convergence rates of gradient methods for high-dimensional statistical recovery – ident: ref10 doi: 10.1109/TSP.2009.2036046 – volume-title: arXiv:2103.13748 year: 2021 ident: ref38 article-title: Compressed gradient tracking methods for decentralized optimization with linear convergence – ident: ref41 doi: 10.1137/19M1259973 – ident: ref4 doi: 10.1017/CBO9781139042918 – start-page: 4447 volume-title: Proc. 32nd NeurIPS ident: ref29 article-title: Sparsified SGD with memory – start-page: 5330 volume-title: Proc. 31st NeurIPS ident: ref5 article-title: Can decentralized algorithms outperform centralized algorithms? A case study for decentralized parallel stochastic gradient descent – ident: ref22 doi: 10.1109/TSP.2020.3031073 – ident: ref31 doi: 10.1109/INFOCOM.2019.8737489 – volume-title: Proc. 9th ICLR ident: ref54 article-title: New bounds for distributed mean estimation and variance reduction – ident: ref8 doi: 10.1109/TSP.2008.927071 – volume-title: Proc. 33rd NeurIPS ident: ref32 article-title: Communication-efficient distributed blockwise momentum SGD with error-feedback – start-page: 9324 volume-title: Proc. 37th ICML ident: ref36 article-title: Quantized decentralized stochastic learning over directed graphs
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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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