Submodular Optimization beyond Nonnegativity: Adaptive Seed Selection in Incentivized Social Advertising

Abstract

Social advertising, also known as social promotion, is a method of promoting products or ideas through the use of influential individuals, known as ``seeds,'' on online social networks. Advertisers and platforms are the main players in this ecosystem, with platforms selling viral engagements, such as ``likes,'' to advertisers by inserting ads into the feeds of seeds. Seeds are given monetary incentives by the platform in exchange for their participation in the campaign, and when a follower of a seed engages with an ad, the platform receives payment from the advertiser. Specifically, at the beginning of a campaign, the advertiser submits a budget to the platform and this budget can be used for two purposes: recruiting seeds and paying for the viral engagements generated by the seeds. Note that the first part of payment goes to the seeds and the latter one is the actual revenue collected by the platform. The challenge for the platform is to select a group of seeds that will generate the most revenue within the budget constraints set by the advertiser. This problem is challenging as the objective function can be non-monotone and may take on negative values. This makes traditional methods of submodular optimization and influence maximization inapplicable. We study this problem under both non-adaptive and adaptive settings, and propose effective solutions for each scenario.