Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06332 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929592023908352 |
|---|---|
| author | Wang, Lei Ren, Zihao Yuan, Deming Shi, Guodong |
| author_facet | Wang, Lei Ren, Zihao Yuan, Deming Shi, Guodong |
| contents | Distributed computing is fundamental to multi-agent systems, with solving distributed linear equations as a typical example. In this paper, we study distributed solvers for network linear equations over a network with node-to-node communication messages compressed as scalar values. Our key idea lies in a dimension compression scheme that includes a dimension-compressing vector and a data unfolding step. The compression vector applies to individual node states as an inner product to generate a real-valued message for node communication. In the unfolding step, such scalar message is then plotted along the subspace generated by the compression vector for the local computations. We first present a compressed consensus flow that relies only on such scalarized communication, and show that linear convergence can be achieved with well excited signals for the compression vector. We then employ such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and prove their linear convergence properties under scalar node communications. With scalar communications, a direct benefit would be the reduced node-to-node communication channel burden for distributed computing. Numerical examples are presented to illustrate the effectiveness of the established theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed Solvers for Network Linear Equations with Scalarized Compression Wang, Lei Ren, Zihao Yuan, Deming Shi, Guodong Systems and Control Distributed computing is fundamental to multi-agent systems, with solving distributed linear equations as a typical example. In this paper, we study distributed solvers for network linear equations over a network with node-to-node communication messages compressed as scalar values. Our key idea lies in a dimension compression scheme that includes a dimension-compressing vector and a data unfolding step. The compression vector applies to individual node states as an inner product to generate a real-valued message for node communication. In the unfolding step, such scalar message is then plotted along the subspace generated by the compression vector for the local computations. We first present a compressed consensus flow that relies only on such scalarized communication, and show that linear convergence can be achieved with well excited signals for the compression vector. We then employ such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and prove their linear convergence properties under scalar node communications. With scalar communications, a direct benefit would be the reduced node-to-node communication channel burden for distributed computing. Numerical examples are presented to illustrate the effectiveness of the established theoretical results. |
| title | Distributed Solvers for Network Linear Equations with Scalarized Compression |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2401.06332 |