Influence Maximization (IM) aims to maximize the number of people that become aware of a product by finding the “best” set of “seed” users to initiate the product advertisement. Unlike most prior arts on the static networks containing fixed number of users, we study the evolving IM in more realistic evolving networks with temporally growing topology. The task of evolving IM, however, is far more challenging over static cases in the sense that the seed selection should consider its impact on future users who will join network during influence diffusion and the probabilities that users influence one another also evolve over time. We address the challenges brought by network evolution through EIM, a newly proposed bandit-based framework that alternates between seed nodes selection and knowledge (i.e., nodes’ growing speed and evolving activation probabilities) learning during network evolution. Remarkably, the EIM framework involves three novel components to handle the uncertainties brought by evolution: (1) A fully adaptive particle learning of nodes’ growing speed for accurately estimating future influenced size, with real growing behaviors delineated by a set of weighted particles. (2) A bandit-based refining method with growing arms to cope with the evolving activation probabilities via growing edges from previous influence diffusion feedbacks. (3) Evo-IMM , an evolving seed selection algorithm, which leverages the Influence Maximization via Martingale (IMM) framework, with the objective to maximize the influence spread to highly attractive users during evolution. Theoretically, the EIM framework returns a regret bound that provably maintains its sublinearity with respect to the growing network size. Empirically, the effectiveness of the EIM framework is also validated with three notable million-scale evolving network datasets possessing complete social relationships and nodes’ joining time. The results confirm the superiority of the EIM framework in terms of an up to 50% larger influenced size over four static baselines.

中文翻译：

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不断发展的网络中不断发展的影响力最大化

影响力最大化 (IM) 旨在通过找到“最佳”“种子”用户来发起产品广告，从而最大限度地增加了解产品的人数。与包含固定数量用户的静态网络上的大多数现有技术不同，我们研究了不断发展的 IM在具有时间增长拓扑的更现实的演化网络中。然而，进化 IM 的任务比静态情况更具挑战性，因为种子选择应考虑其对在影响扩散期间将加入网络的未来用户的影响，并且用户相互影响的概率也会随着时间而演变。我们通过 EIM 解决网络演化带来的挑战，EIM 是一种新提出的基于强盗的框架，它在网络演化期间在种子节点选择和知识（即节点的增长速度和不断演化的激活概率）学习之间交替进行。值得注意的是，EIM 框架涉及三个新组件来处理进化带来的不确定性：（1）节点增长速度的完全自适应粒子学习，用于准确估计未来影响大小，具有由一组加权粒子描绘的真实增长行为。(2) 一种基于强盗的改进方法，具有增长的臂，以通过来自先前影响扩散反馈的增长边缘来应对不断变化的激活概率。(3)Evo-IMM，一种不断发展的种子选择算法，它利用通过 Martingale （IMM）框架的影响最大化，目标是在进化过程中最大限度地传播给极具吸引力的用户的影响力。从理论上讲，EIM 框架返回一个遗憾界限，该界限可证明保持其相对于不断增长的网络规模的次线性。经验上，EIM 框架的有效性也通过三个具有完整社会关系和节点加入时间的值得注意的百万级演化网络数据集得到验证。结果证实了 EIM 框架的优越性，其影响大小比四个静态基线大 50%。