The $s$-Energy and Its Applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915810054766592 |
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| author | Chazelle, Bernard Karntikoon, Kritkorn |
| author_facet | Chazelle, Bernard Karntikoon, Kritkorn |
| contents | Many multi-agent systems evolve by repeatedly updating each state to a weighted average of its neighbors, a process known as averaging dynamics, whose behavior becomes difficult to analyze when the interaction network varies over time. In recent years, the $s$-energy has emerged as a useful tool for bounding the convergence rates of such systems, complementing the classical techniques that rely on fixed graphs. We derive new bounds on the $s$-energy under minimal connectivity assumptions. As a consequence, we obtain convergence guarantees for several models of collective dynamics and resolve a number of open questions in the areas. Our results highlight the dependence of the $s$-energy on the connectivity of the underlying networks and use it to explain the exponential gap in the convergence rates of stationary and time-varying consensus systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $s$-Energy and Its Applications Chazelle, Bernard Karntikoon, Kritkorn Optimization and Control Multiagent Systems Many multi-agent systems evolve by repeatedly updating each state to a weighted average of its neighbors, a process known as averaging dynamics, whose behavior becomes difficult to analyze when the interaction network varies over time. In recent years, the $s$-energy has emerged as a useful tool for bounding the convergence rates of such systems, complementing the classical techniques that rely on fixed graphs. We derive new bounds on the $s$-energy under minimal connectivity assumptions. As a consequence, we obtain convergence guarantees for several models of collective dynamics and resolve a number of open questions in the areas. Our results highlight the dependence of the $s$-energy on the connectivity of the underlying networks and use it to explain the exponential gap in the convergence rates of stationary and time-varying consensus systems. |
| title | The $s$-Energy and Its Applications |
| topic | Optimization and Control Multiagent Systems |
| url | https://arxiv.org/abs/2410.22341 |