A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

中文翻译：

---

通过非凸局部搜索改变说服敏感性的意见动态优化

社会心理学的长期工作研究了人们对说服的敏感性的变化——他们愿意在多大程度上改变他们对某个话题的看法。这组文献提出了一个有趣的观点，即关于网络中互动各方形成意见的理论模型：除了考虑直接改变人们内在意见的干预措施外，考虑改变人们对说服的敏感性的干预措施也是很自然的。在这项工作中，受这一事实的启发，我们提出了一个影响优化问题。具体来说，我们采用了一种流行的社会意见动态模型，其中每个代理都有一些固定的先天意见，以及衡量其对其先天意见重要性的阻力；代理人通过一个迭代过程影响彼此的意见。在一定条件下，这个迭代过程会收敛到某个均衡的意见向量。对于问题的未预算变体，目标是修改任意数量的代理（在某个给定范围内）的阻力，以使平衡意见的总和最小化；对于预算变体，此外，算法预先限制了可以修改阻力的代理数量。我们证明了目标函数通常是非凸的。因此，在这项工作的早期版本（Abebe 等人，KDD'18）中将问题表述为凸程序可能存在潜在的正确性问题。相反，我们分析了目标函数的结构，并表明任何局部最优也是全局最优，这在某种程度上令人惊讶，因为目标函数可能不是凸的。此外，我们将迭代过程和局部搜索范式结合起来，设计出非常有效的算法，可以在包含数百万个节点的大规模图上最优地解决问题的未预算变体。最后，我们针对问题的预算变体提出并通过实验评估了一系列启发式方法。