Social Learning Algorithms In Complex Networks

It is well known that opinions decide actions and decisions to a certain extent.Therefore, analyzing, interpreting, and even forecasting the formation and evolution ofopinionsareimportantresearchtopics. Sociallearningtheorymainlyfocusesonsocialfactors afecting the opinion formation and evolution. By establishing and analyzingmathematical models, it studies how social environment and collective interaction-s infuence the opinion formation. Recently, as the the fourish of study on complexsystems and complex networks, social learning which is an important research areaof collective behavior in social networks has attracted signifcant attention from re-searchers in diferent felds. This dissertation surveys the recent advances in sociallearning theory and investigates how social structure and opinion updating rules afectopinion formation based on multi-agent models. The main works are summarized asfollows:1. Investigationonsociallearninginrandomnetworkswithsimilarity-basedlinks.A typical assumption in the well-known Hegselmann-Krause model (the HK model forshort) is that agents only consider those who have similar opinions as their neighborsand completely ignore other agents outside the bound of confdence. In the real world,individuals are indeed prone to communicate with those who have similar opinions,while they may also keep in touch with a few friends holding quite diferent opinions.Based on this fact, a social network structure with random neighbors outside the boundof confdence is considered. It is shown that, as long as the bound of confdence isstrictlypositive, opinionsofthepopulationwillreachaconsensusinboundedtime. Anupper bound of convergence time is given. If the infuence of bound of confdence iscompletely ignored, i.e., all neighbors are selected randomly according to a similarity-based probability, opinions will also converge to a consensus, but in the probabilitysense. Simulations further show that agents communicating beyond the diference on opinions will reach a consensus fast.2. Investigation on social learning in bounded-confdence networks with endoge-nous leaders. Consistency and correctness of opinions are two important aspects stud-ied in the literature. As for the HK model, there is no conception of correct opinion,and thus, it mainly focus on the consistency of opinions. To study the correctness ofopinions in the HK model, a constant value in the opinion space is set to be the correctopinion. Whenanindividualconfrontsthecorrectopinion, sheisboundedlyconfdent,i.e., she will consider and be infuenced by the correct opinion only if the correct opin-ion is inside her bound of confdence. Any agents endowing positive weights to thecorrect opinion are called endogenous leaders, and the weights represent their learningspeed. For any pair of bound of confdence and position of correct opinion, a possiblerange of learning speed of the leaders to guarantee the whole group learning the cor-rect opinion is provided. It is found that there always exists a suitable learning speedleading the whole group to a consensus on the correct opinion as long as the wholegroup converge to a consensus in the absence of the infuence of correct opinion.3. Investigate on social learning in bounded-confdence networks with hetero-geneous agents and observable signals. Bayesian updating based on observed signalsprovides a reasonable realization of the infuence of correct opinion. A social learningalgorithm with observable signals is studied in heterogeneous networks with boundedconfdence, where agents are classifed as leaders and followers. It is shown that thewhole group can learn the correct opinion only under a relative large bound of con-fdence; otherwise, the agents will be divided into multiple isolated clusters based ontheir opinions, and only part of them can learn the correct opinion. In addition, thelearning speed of leaders has signifcant infuence on the learning performance. Thereexits a trade-of: the higher the learning speed, the shorter the time needed for the w-hole group to achieve a steady state, and on the other hand, the higher the speed, thelower the proportion of agents learning the correct opinion.4. Investigation on social learning in time-varying connected networks with ob-servable signals. The topology in bounded-confdence networks is decided by indi-viduals’ opinions, where the connectivity of networks cannot be guaranteed, and thus,some agents might not be able to learn the correct opinion. Two sorts of time-varying networks with connectivity preserved to certain extents are considered. It is shownthat,undercertainassumptionssuchas(jointly)strongconnectivityandlower-boundedpositive weights, the opinions of the population can reach a consensus. Furthermore,if there exists no state that is observationally equivalent to the true state, the commonopinion is the correct opinion.