We study a family online influence maximization problems where in a sequence of rounds $t=1,\ldots,T$, a decision maker selects one from a large number of agents with the goal of maximizing influence. Upon choosing an agent, the decision maker shares a piece of information with the agent, which information then spreads in an unobserved network over which the agents communicate. The goal of the decision maker is to select the sequence of agents in a way that the total number of influenced nodes in the network. In this work, we consider a scenario where the networks are generated independently for each $t$ according to some fixed but unknown distribution, so that the set of influenced nodes corresponds to the connected component of the random graph containing the vertex corresponding to the selected agent. Furthermore, we assume that the decision maker only has access to limited feedback: instead of making the unrealistic assumption that the entire network is observable, we suppose that the available feedback is generated based on a small neighborhood of the selected vertex. Our results show that such partial local observations can be sufficient for maximizing global influence. We model the underlying random graph as a sparse inhomogeneous Erd\H{o}s--R\'enyi graph, and study three specific families of random graph models in detail: stochastic block models, Chung--Lu models and Kronecker random graphs. We show that in these cases one may learn to maximize influence by merely observing the degree of the selected vertex in the generated random graph. We propose sequential learning algorithms that aim at maximizing influence, and provide their theoretical analysis in both the subcritical and supercritical regimes of all considered models.

翻译：我们研究的是家庭在线影响最大化问题, 在一个回合序列中, $t=1,\ldots,T$, 决策人从大量代理人中选择一个, 目的是最大限度地发挥影响力。 在选择一个代理人时, 决策人与代理共享一条信息, 信息在代理商通信的未观测的网络中传播。 决策人的目标是选择代理商的序列, 其方式为网络中受影响的节点的总数。 在这项工作中, 我们考虑一个假设, 网络根据某些固定但未知的分布, 独立为每美元创建一个。 因此, 受影响的节点组与含有与选定代理人相对的顶点的随机图的连接部分相匹配。 此外, 我们假设, 决策人只能获得有限的反馈: 不现实地假设整个网络是可见的, 我们假设, 可获得的反馈是根据所选的直径直径直的一小块区域。 我们的观测结果显示, 局部的当地观察可以充分实现全球影响力最大化。 我们用一个随机的图表模型, 也就是一个直径直方的直径直方模型, 和直径直径直方的模型, 以直方的直方的直方的直方的直方模型, 以正方的直方的直方形模型显示一个直方的直方的直方形模型显示, 。