Optimal selection of the most informative nodes for a noisy DeGroot model with stubborn agents
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908623631810560 |
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| author | Raineri, Roberta Como, Giacomo Fagnani, Fabio |
| author_facet | Raineri, Roberta Como, Giacomo Fagnani, Fabio |
| contents | Finding the optimal subset of individuals to observe in order to obtain the best estimate of the average opinion of a society is a crucial problem in a wide range of applications, including policy-making, strategic business decisions, and the analysis of sociological trends. We consider the opinion vector X to be updated according to a DeGroot opinion dynamical model with stubborn agents, subject to perturbations from external random noise, which can be interpreted as transmission errors. The objective function of the optimization problem is the variance reduction achieved by observing the equilibrium opinions of a subset K of agents. We demonstrate that, under this specific setting, the objective function exhibits the property of submodularity. This allows us to effectively design a Greedy Algorithm to solve the problem, significantly reducing its computational complexity. Simple examples are provided to validate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08622 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal selection of the most informative nodes for a noisy DeGroot model with stubborn agents Raineri, Roberta Como, Giacomo Fagnani, Fabio Optimization and Control Dynamical Systems Finding the optimal subset of individuals to observe in order to obtain the best estimate of the average opinion of a society is a crucial problem in a wide range of applications, including policy-making, strategic business decisions, and the analysis of sociological trends. We consider the opinion vector X to be updated according to a DeGroot opinion dynamical model with stubborn agents, subject to perturbations from external random noise, which can be interpreted as transmission errors. The objective function of the optimization problem is the variance reduction achieved by observing the equilibrium opinions of a subset K of agents. We demonstrate that, under this specific setting, the objective function exhibits the property of submodularity. This allows us to effectively design a Greedy Algorithm to solve the problem, significantly reducing its computational complexity. Simple examples are provided to validate our results. |
| title | Optimal selection of the most informative nodes for a noisy DeGroot model with stubborn agents |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2504.08622 |