Tsitsiklis J N, Athans M. Convergence and asymptomatic agreement on distributed decision-making problems. IEEE Trans Contr, 1984, 29: 42-50 Huang M, Manton J H. Coordination and consensus of agents connected with noisy measures: stochastic algorithms and asymptomatic behavior. SIAM J Control Opt, 2009, 48:134-161 Social Sampling is a new randomized communication protocol that draws on social communication to form an opinion on social networks. In a typical social sampling algorithm, each agent holds a sample of the empirical distribution of social opinions at the first time and works with other agents in a distributed manner to estimate the initial empirical distribution by randomly scanning a message of the current distribution estimate. In this post, we focus on analyzing the theoretical properties of the social sampling algorithm distributed via random networks. First, we propose a framework based on the stochastic approach to study the asymptomatic properties of the algorithm. Then, under mild conditions, we prove that estimates of all active substances converge towards a common random distribution, which consists of initial empirical distribution and accumulation of quantitiive errors. Moreover, by optimizing the parameters of the algorithm, we prove the strong consistency, namely that the distribution estimates of agents almost surely converge with the initial empirical distribution. In addition, the asymptomatic normality of the estimation error generated by distributed social sampling algorithms is addressed.
Finally, we provide a numerical simulation to validate the theoretical results of this contribution. Frasca P, Ishii H, Ravazzi C, et al. Randomised algorithms distributed for opinion formation, centrality calculation and electrical system estimation: a tutorial. Eur J Control, 2015, 24: 2-13 Wang Y H, Lin P, Hong Y G. Regression estimate distributed with incomplete data in multi-agent networks. Sci China Inf Sci, 2018, 61: 092202 Borkar V, Varaiya P. Asymptotic agreement in distributed estimate. IEEE Trans Contr, 1982, 27: 650-655 Ceragioli F, Frasca P.
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