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Problem definition: Corporate brands, grassroots activists, and ordinarycitizens all routinely employ Word-of-mouth (WoM) diffusion to promote productsand instigate social change. Our work models the formation and spread ofnegative attitudes via WoM on a social network represented by a directed graph.In an online learning setting, we examine how an agent could simultaneouslylearn diffusion parameters and choose sets of seed users to initiate diffusionsand maximize positive influence. In contrast to edge-level feedback, in whichan agent observes the relationship (edge) through which a user (node) isinfluenced, we more realistically assume node-level feedback, where an agentonly observes when a user is influenced and whether that influence is positiveor negative. Methodology/results: We propose a new class of negativity-awareLinear Threshold Models. We show that in these models, the expected positiveinfluence spread is a monotone submodular function of the seed set. Therefore,when maximizing positive influence by selecting a seed set of fixed size, agreedy algorithm can guarantee a solution with a constant approximation ratio.For the online learning setting, we propose an algorithm that runs in epochs ofgrowing lengths, each consisting of a fixed number of exploration roundsfollowed by an increasing number of exploitation rounds controlled by ahyperparameter. Under mild assumptions, we show that our algorithm achievesasymptotic expected average scaled regret that is inversely related to anyfractional constant power of the number of rounds. Managerial implications:During seed selection, our negativity-aware models and algorithms allow WoMcampaigns to discover and best account for characteristics of local users andpropagated content. We also give the first algorithms with regret guaranteesfor influence maximization under node-level feedback.

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