Recurrent averaging inequalities in multi-agent control and social dynamics modeling

Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a flock, or the measurement of a sensor within a sensor network. This value is updated, at each iteration, to a weighted average of itself and of the values of the adjacent agents. It is well known that, under natural assumptions on the network's graph connectivity, this local averaging procedure eventually leads to global consensus, or synchronization of the values at all nodes. Applications of iterative averaging include, but are not limited to, algorithms for distributed optimization, for solution of linear and nonlinear equations, for multi-robot coordination and for opinion formation in social groups. Although these algorithms have similar structures, the mathematical techniques used for their analysis are diverse, and conditions for their convergence and differ from case to case. In this paper, we review many of these algorithms and we show that their properties can be analyzed in a unified way by using a novel tool based on recurrent averaging inequalities (RAIs). We develop a theory of RAIs and apply it to the analysis of several important multi-agent algorithms recently proposed in the literature

Recurrent Averaging Inequalities in Multi-Agent Control and Social Dynamics Modeling

Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a flock, or the measurement of a sensor within a sensor network. This value is updated, at each iteration, to a weighted average of itself and of the values of the adjacent agents. It is well known that, under natural assumptions on the network's graph connectivity, this local averaging procedure eventually leads to global consensus, or synchronization of the values at all nodes. Applications of iterative averaging include, but are not limited to, algorithms for distributed optimization, for solution of linear and nonlinear equations, for multi-robot coordination and for opinion formation in social groups. Although these algorithms have similar structures, the mathematical techniques used for their analysis are diverse, and conditions for their convergence and differ from case to case. In this paper, we review many of these algorithms and we show that their properties can be analyzed in a unified way by using a novel tool based on recurrent averaging inequalities (RAIs). We develop a theory of RAIs and apply it to the analysis of several important multi-agent algorithms recently proposed in the literature

Differential Inequalities in Multi-Agent Coordination and Opinion Dynamics Modeling

Distributed algorithms of multi-agent coordination have attracted substantial attention from the research community; the simplest and most thoroughly studied of them are consensus protocols in the form of differential or difference equations over general time-varying weighted graphs. These graphs are usually characterized algebraically by their associated Laplacian matrices. Network algorithms with similar algebraic graph theoretic structures, called being of Laplacian-type in this paper, also arise in other related multi-agent control problems, such as aggregation and containment control, target surrounding, distributed optimization and modeling of opinion evolution in social groups. In spite of their similarities, each of such algorithms has often been studied using separate mathematical techniques. In this paper, a novel approach is offered, allowing a unified and elegant way to examine many Laplacian-type algorithms for multi-agent coordination. This approach is based on the analysis of some differential or difference inequalities that have to be satisfied by the some "outputs" of the agents (e.g. the distances to the desired set in aggregation problems). Although such inequalities may have many unbounded solutions, under natural graphic connectivity conditions all their bounded solutions converge (and even reach consensus), entailing the convergence of the corresponding distributed algorithms. In the theory of differential equations the absence of bounded non-convergent solutions is referred to as the equation's dichotomy. In this paper, we establish the dichotomy criteria of Laplacian-type differential and difference inequalities and show that these criteria enable one to extend a number of recent results, concerned with Laplacian-type algorithms for multi-agent coordination and modeling opinion formation in social groups.Comment: accepted to Automatic

Bayesian learning without recall

We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the actions of their neighboring agents at each time. Successive applications of Bayes rule to the entire history of past observations lead to forebodingly complex inferences: due to lack of knowledge about the global network structure, and unavailability of private observations, as well as third party interactions preceding every decision. Such difficulties make Bayesian updating of beliefs an implausible mechanism for social learning. To address these complexities, we consider a Bayesian without Recall model of inference. On the one hand, this model provides a tractable framework for analyzing the behavior of rational agents in social networks. On the other hand, this model also provides a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for the structure of the action space and utility functions for such agents and investigate the properties of learning, convergence, and consensus in special cases

Temporal Emotion Dynamics in Social Networks

[ES] El análisis de sentimientos en redes sociales se ha estudiado ampliamente durante la última década. A pesar de ello, las distintas categorías de sentimientos no se consideran adecuadamente en muchos casos, y el estudio de patrones de difusión de las emociones es limitado. Por lo tanto, comprender la importancia de emociones específicas será más beneficioso para diversas actividades de marketing, toma de decisiones empresariales y campañas políticas. Esta tesis doctoral se centra en el diseño de un marco teórico para analizar el amplio espectro de sentimientos y explicar cómo se propagan las emociones utilizando conceptos de redes temporales y multicapa. Particularmente, nuestro objetivo es proporcionar información sobre el modelado de la influencia de las emociones y como esta afecta a los problemas de estimación de las emociones y a la naturaleza dinámica temporal en la conversación social. Para mostrar la eficacia del modelo propuesto, se han recopilado publicaciones relacionadas con diferentes eventos de Twitter y hemos construido una estructura de red temporal sobre la conversación. En primer lugar, realizamos un análisis de sentimientos adoptando un enfoque basado en el léxico y en el modelo circunflejo de emociones de Russell que mejora la efectividad de la caracterización del sentimiento. A partir de este análisis investigamos la dinámica social de las emociones presente en las opiniones de los usuarios analizando diferentes características de influencia social. A continuación, diseñamos un modelo estocástico temporal basado en emociones para investigar el patrón de participación de los usuarios y predecir las emociones significativas. Nuestra contribución final es el desarrollo de un modelo de influencia secuencial basado en emociones mediante la utilización de redes neuronales recurrentes que permiten predecir emociones de una manera más completa. Finalmente, el documento presenta algunas conclusiones y también describe las direcciones de investigación futuras.[CA] L'anàlisi de sentiments en xarxes socials s'ha estudiat àmpliament durant l'última dècada. Malgrat això, les diferents categories de sentiments no es consideren adequadament en molts casos, i l'estudi de patrons de difusió de les emocions és limitat. Per tant, comprendre la importància d'emocions específiques serà més beneficiós per a diverses activitats de màrqueting, presa de decisions empresarials i campanyes polítiques. Aquesta tesi doctoral se centra en el disseny d'un marc teòric per a analitzar l'ampli espectre de sentiments i explicar com es propaguen les emocions utilitzant conceptes de xarxes temporals i multicapa. Particularment, el nostre objectiu és proporcionar informació sobre el modelatge de la influència de les emocions i com aquesta afecta als problemes d'estimació de les emocions i a la naturalesa dinàmica temporal en la conversa social. Per a mostrar l'eficàcia del model proposat, s'han recopilat publicacions relacionades amb diferents esdeveniments de Twitter i hem construït una estructura de xarxa temporal sobre la conversa. En primer lloc, realitzem una anàlisi de sentiments adoptant un enfocament basat en el lèxic i en el model circumflex d'emocions de Russell que millora l'efectivitat de la caracterització del sentiment. A partir d'aquesta anàlisi investiguem la dinàmica social de les emocions present en les opinions dels usuaris analitzant diferents característiques d'influència social. A continuació, dissenyem un model estocàstic temporal basat en emocions per a investigar el patró de participació dels usuaris i predir les emocions significatives. La nostra contribució final és el desenvolupament d'un model d'influència seqüencial basat en emocions mitjançant la utilització de xarxes neuronals recurrents que permeten predir emocions d'una manera més completa. Finalment, el document presenta algunes conclusions i també descriu les direccions d'investigació futures.[EN] Sentiment analysis in social networks has been widely analysed over the last decade. Despite the amount of research done in sentiment analysis in social networks, the distinct categories are not appropriately considered in many cases, and the study of dissemination patterns of emotions is limited. Therefore, understanding the significance of specific emotions will be more beneficial for various marketing activities, policy-making decisions and political campaigns. The current PhD thesis focuses on designing a theoretical framework for analyzing the broad spectrum of sentiments and explain how emotions are propagated using concepts from temporal and multilayer networks. More precisely, our goal is to provide insights into emotion influence modelling that solves emotion estimation problems and its temporal dynamics nature on social conversation. To exhibit the efficacy of the proposed model, we have collected posts related to different events from Twitter and build a temporal network structure over the conversation. Firstly, we perform sentiment analysis with the adaptation of a lexicon-based approach and the circumplex model of affect that enhances the effectiveness of the sentiment characterization. Subsequently, we investigate the social dynamics of emotion present in users' opinions by analyzing different social influential characteristics. Next, we design a temporal emotion-based stochastic model in order to investigate the engagement pattern and predict the significant emotions. Our ultimate contribution is the development of a sequential emotion-based influence model with the advancement of recurrent neural networks. It offers to predict emotions in a more comprehensive manner. Finally, the document presents some conclusions and also outlines future research directions.Naskar, D. (2022). Temporal Emotion Dynamics in Social Networks [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/180997TESI

On a Network Centrality Maximization Game

We study a network formation game where $n$ players, identified with the nodes of a directed graph to be formed, choose where to wire their outgoing links in order to maximize their PageRank centrality. Specifically, the action of every player $i$ consists in the wiring of a predetermined number $d_i$ of directed out-links, and her utility is her own PageRank centrality in the network resulting from the actions of all players. We show that this is a potential game and that the best response correspondence always exhibits a local structure in that it is never convenient for a node $i$ to link to other nodes that are at incoming distance more than $d_i$ from her. We then study the equilibria of this game determining necessary conditions for a graph to be a (strict, recurrent) Nash equilibrium. Moreover, in the homogeneous case, where players all have the same number $d$ of out-links, we characterize the structure of the potential maximizing equilibria and, in the special cases $d=1$ and $d=2$, we provide a complete classification of the set of (strict, recurrent) Nash equilibria. Our analysis shows in particular that the considered formation mechanism leads to the emergence of undirected and disconnected or loosely connected networks.Comment: 42 pages, 11 figure