TY - JOUR
T1 - Distributed learning of average belief over networks using sequential observations
AU - Zhang, Kaiqing
AU - Liu, Yang
AU - Liu, Ji
AU - Liu, Mingyan
AU - Başar, Tamer
N1 - The work of K. Zhang and T. Başar was supported in part by Office of Naval Research (ONR), United States of America, MURI Grant N00014-16-1-2710 , and in part by US Army Research Office (ARO) Grant W911NF-16-1-0485 . The work of M. Liu is partially supported by the National Science Foundation (NSF), United States of America, under grants ECCS 1446521 , CNS-1646019 , and CNS-1739517 . The material in this paper was partially presented at the 2017 American Control Conference, May 24-26, 2017, Seattle, WA, USA. This paper was recommended for publication in revised form by Associate Editor Antonis Papachristodoulou under the direction of Editor Christos G. Cassandras
PY - 2020/5
Y1 - 2020/5
N2 - This paper addresses the problem of distributed learning of average belief with sequential observations, in which a network of n>1 agents aim to reach a consensus on the average value of their beliefs, by exchanging information only with their neighbors. Each agent has sequentially arriving samples of its belief in an online manner. The neighbor relationships among the n agents are described by a graph which is possibly time-varying, whose vertices correspond to agents and whose edges depict neighbor relationships. Two distributed online algorithms are introduced for undirected and directed graphs, which are both shown to converge to the average belief almost surely. Moreover, the sequences generated by both algorithms are shown to reach consensus with an O(1∕t) rate with high probability, where t is the number of iterations For undirected graphs, the corresponding algorithm is modified for the case with quantized communication and limited precision of the division operation. It is shown that the modified algorithm causes all n agents to either reach a quantized consensus or enter a small neighborhood around the average of their beliefs. Numerical simulations are then provided to corroborate the theoretical results.
AB - This paper addresses the problem of distributed learning of average belief with sequential observations, in which a network of n>1 agents aim to reach a consensus on the average value of their beliefs, by exchanging information only with their neighbors. Each agent has sequentially arriving samples of its belief in an online manner. The neighbor relationships among the n agents are described by a graph which is possibly time-varying, whose vertices correspond to agents and whose edges depict neighbor relationships. Two distributed online algorithms are introduced for undirected and directed graphs, which are both shown to converge to the average belief almost surely. Moreover, the sequences generated by both algorithms are shown to reach consensus with an O(1∕t) rate with high probability, where t is the number of iterations For undirected graphs, the corresponding algorithm is modified for the case with quantized communication and limited precision of the division operation. It is shown that the modified algorithm causes all n agents to either reach a quantized consensus or enter a small neighborhood around the average of their beliefs. Numerical simulations are then provided to corroborate the theoretical results.
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U2 - 10.1016/j.automatica.2020.108857
DO - 10.1016/j.automatica.2020.108857
M3 - Article
AN - SCOPUS:85079330960
SN - 0005-1098
VL - 115
JO - Automatica
JF - Automatica
M1 - 108857
ER -