| Summary: | We study a message passing network where nodes keep a numeric attitude toward a subject. Messages are created by a message factory and each is sent to a random seed-node, which then gets eventually propagated in the network. Each message has some information about the subject, which is interpreted by the receiving node based on its features. Hence, the same message could be interpreted quite differently by two different nodes. Once a message is interpreted, the attitude of the node toward the subject is updated. In this setting, the thesis is that an external agent can influence (in a desired way) the average attitude of the network, by sending the messages to specific nodes (rather than sending them randomly) based on the message content. We call this agent a leader which its goal is to minimize (maximize) the average attitude of the network, and its actions are choosing one of the seed-nodes for a given message. The leader does not have any information about the nodes in advance, instead, it eventually learns the interests of the seed-nodes through sending messages and receiving the feedback of the network. We formulate this as a contextual bandit problem and study the effectiveness of a leader in different network configurations. Moreover, we study the case that there are two adversarial leaders, and present different policies and evaluate their effectiveness. Finally, we study the leader's performance when there are dynamic changes in the nodes features and network's topology.
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