Quantized Distributed Gradient Tracking Algorithm With Linear Convergence in Directed Networks

Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized distributed optimization algorithms can only converge sublinearly. To achieve linear convergence, this paper proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to minimize a finite sum of local objective functions over directed networks. Moreover, we explicitly derive the update rule for the number of quantization levels, and prove that Q-DGT can converge linearly even when the exchanged variables are respectively one bit. Numerical results also confirm the efficiency of the proposed algorithm.

[1]  Na Li,et al.  Harnessing smoothness to accelerate distributed optimization , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[2]  Usman A. Khan,et al.  A Linear Algorithm for Optimization Over Directed Graphs With Geometric Convergence , 2018, IEEE Control Systems Letters.

[3]  Guo Chen,et al.  Computation-Efficient Distributed Algorithm for Convex Optimization Over Time-Varying Networks With Limited Bandwidth Communication , 2020, IEEE Transactions on Signal and Information Processing over Networks.

[4]  Tamer Başar,et al.  Distributed Discrete-Time Optimization in Multiagent Networks Using Only Sign of Relative State , 2017, IEEE Transactions on Automatic Control.

[5]  Lihua Xie,et al.  Distributed Consensus With Limited Communication Data Rate , 2011, IEEE Transactions on Automatic Control.

[6]  Angelia Nedic,et al.  Distributed optimization over time-varying directed graphs , 2013, 52nd IEEE Conference on Decision and Control.

[7]  Lihua Xie,et al.  Distributed Online Optimization for Multi-Agent Networks With Coupled Inequality Constraints , 2018, IEEE Transactions on Automatic Control.

[8]  F. Lewis,et al.  A Unified Strategy for Solution Seeking in Graphical $N$-Coalition Noncooperative Games , 2017, IEEE Transactions on Automatic Control.

[9]  Martin Jaggi,et al.  A Linearly Convergent Algorithm for Decentralized Optimization: Sending Less Bits for Free! , 2020, AISTATS.

[10]  José M. F. Moura,et al.  Fast Distributed Gradient Methods , 2011, IEEE Transactions on Automatic Control.

[11]  Asuman E. Ozdaglar,et al.  Distributed Subgradient Methods for Multi-Agent Optimization , 2009, IEEE Transactions on Automatic Control.

[12]  Cheng Wu,et al.  Distributed Convex Optimization with Inequality Constraints over Time-Varying Unbalanced Digraphs , 2016, IEEE Transactions on Automatic Control.

[13]  Martin J. Wainwright,et al.  Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling , 2010, IEEE Transactions on Automatic Control.

[14]  Brian D. O. Anderson,et al.  Distributed Algorithms with Finite Data Rates that Solve Linear Equations , 2020, SIAM J. Optim..

[15]  Shi Pu.  A Robust Gradient Tracking Method for Distributed Optimization over Directed Networks , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[16]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[17]  Na Li,et al.  On Maintaining Linear Convergence of Distributed Learning and Optimization Under Limited Communication , 2019, IEEE Transactions on Signal Processing.

[18]  Angelia Nedic,et al.  Distributed Gradient Methods for Convex Machine Learning Problems in Networks: Distributed Optimization , 2020, IEEE Signal Processing Magazine.

[19]  Yiguang Hong,et al.  Quantized Subgradient Algorithm and Data-Rate Analysis for Distributed Optimization , 2014, IEEE Transactions on Control of Network Systems.

[20]  Lihua Xie,et al.  Convergence of Asynchronous Distributed Gradient Methods Over Stochastic Networks , 2018, IEEE Transactions on Automatic Control.

[21]  Lihua Xie,et al.  Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[22]  Keyou You,et al.  Distributed Conjugate Gradient Tracking for Resource Allocation in Unbalanced Networks , 2019, ArXiv.

[23]  Lihua Xie,et al.  Survey on Localization Systems and Algorithms for Unmanned Systems , 2020, Unmanned Syst..

[24]  Thinh T. Doan,et al.  Convergence Rates of Distributed Gradient Methods Under Random Quantization: A Stochastic Approximation Approach , 2021, IEEE Transactions on Automatic Control.

[25]  Carlo Fischione,et al.  Convergence of Limited Communication Gradient Methods , 2018, IEEE Transactions on Automatic Control.

[26]  Jiliang Tang,et al.  Linear Convergent Decentralized Optimization with Compression , 2021, ICLR.

[27]  Wei Shi,et al.  Push–Pull Gradient Methods for Distributed Optimization in Networks , 2021, IEEE Transactions on Automatic Control.