Randomized Pricing with Deferred Acceptance for Revenue Maximization with Submodular Objectives

A lot of applications in web economics need to maximize the revenue under a budget for payments and also guarantee the truthfulness of users, so Budget-Feasible Mechanism (BFM) Design has aroused great interests during last decade. Most of the existing BFMs concentrate on maximizing a monotone submodular function subject to a knapsack constraint, which is insufficient for many applications with complex objectives or constraints. Observing this, the recent studies (e.g., [4, 5, 11]) have considered non-monotone submodular objectives or more complex constraints such as a k-system constraint. In this study, we follow this line of research and propose truthful BFMs with improved performance bounds for non-monotone submodular objectives with or without a k-system constraint. Our BFMs leverage the idea of providing random prices to users while deferring the decision on the final winning set, and are also based on a novel randomized algorithm for the canonical constrained submodular maximization problem achieving better performance bounds compared to the state-of-the-art. Finally, the effectiveness and efficiency of our approach are demonstrated by extensive experiments on several applications about social network marketing, crowdsourcing and personalized recommendation.