Online Learning and Optimization Under a New Linear-Threshold Model with Negative Influence

Abstract

Problem definition: Corporate brands, grassroots activists, and ordinary citizens all routinely employ Word-of-mouth (WoM) diffusion to promote products and instigate social change. Our work models the formation and spread of negative attitudes via WoM on a social network represented by a directed graph. In an online learning setting, we examine how an agent could simultaneously learn diffusion parameters and choose sets of seed users to initiate diffusions and maximize positive influence. In contrast to edge-level feedback, in which an agent observes the relationship (edge) through which a user (node) is influenced, we more realistically assume node-level feedback, where an agent only observes when a user is influenced and whether that influence is positive or negative. Methodology/results: We propose a new class of negativity-aware Linear Threshold Models. We show that in these models, the expected positive influence spread is a monotone submodular function of the seed set. Therefore, when maximizing positive influence by selecting a seed set of fixed size, a greedy algorithm can guarantee a solution with a constant approximation ratio. For the online learning setting, we propose an algorithm that runs in epochs of growing lengths, each consisting of a fixed number of exploration rounds followed by an increasing number of exploitation rounds controlled by a hyperparameter. Under mild assumptions, we show that our algorithm achieves asymptotic expected average scaled regret that is inversely related to any fractional constant power of the number of rounds. Managerial implications: During seed selection, our negativity-aware models and algorithms allow WoM campaigns to discover and best account for characteristics of local users and propagated content. We also give the first algorithms with regret guarantees for influence maximization under node-level feedback.