تقرير
On the Optimal Communication Weights in Distributed Optimization Algorithms
| العنوان: | On the Optimal Communication Weights in Distributed Optimization Algorithms |
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| المؤلفون: | Colla, Sebastien, Hendrickx, Julien M. |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Multiagent Systems |
| الوصف: | We establish that in distributed optimization, the prevalent strategy of minimizing the second-largest eigenvalue modulus (SLEM) of the averaging matrix for selecting communication weights, while optimal for existing theoretical performance bounds, is generally not optimal regarding the exact worst-case performance of the algorithms. This exact performance can be computed using the Performance Estimation Problem (PEP) approach. We thus rely on PEP to formulate an optimization problem that determines the optimal communication weights for a distributed optimization algorithm deployed on a specified undirected graph. Our results show that the optimal weights can outperform the weights minimizing the second-largest eigenvalue modulus (SLEM) of the averaging matrix. This suggests that the SLEM is not the best characterization of weighted network performance for decentralized optimization. Additionally, we explore and compare alternative heuristics for weight selection in distributed optimization. Comment: 7 pages. Submitted to MTNS |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2402.05705Test |
| رقم الانضمام: | edsarx.2402.05705 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |