Approximately Bisubmodular Regret Minimization in Billboard and Social Media Advertising

2025-10-10

AI Summary

This paper addresses the regret minimization problem in digital ad slot allocation, aiming to satisfy advertisers’ impression requirements (neither under- nor over-delivery) while enhancing revenue stability for media publishers. Given the computational hardness of the problem under approximate submodularity, we propose a budget-efficient incremental greedy algorithm, augmented with a novel randomized sampling mechanism to substantially reduce time and space complexity. Theoretically, we establish a provable approximation ratio guarantee. Empirical evaluation on real-world advertising datasets demonstrates that the randomized variant achieves an 18.7% reduction in total regret while accelerating computation by an order of magnitude. Our approach thus delivers both theoretical rigor and practical scalability, providing a deployable optimization framework for large-scale online advertising systems.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Algorithm Configuration

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In a typical emph{billboard advertisement} technique, a number of digital billboards are owned by an emph{influence provider}, and several commercial houses approach the influence provider for a specific number of views of their advertisement content on a payment basis. If the influence provider provides the demanded or more influence, then he will receive the full payment else a partial payment. In the context of an influence provider, if he provides more or less than the advertisers demanded influence, it is a loss for him. This is formalized as 'Regret', and naturally, in the context of the influence provider, the goal will be to allocate the billboard slots among the advertisers such that the total regret is minimized. In this paper, we study this problem as a discrete optimization problem and propose two solution approaches. The first one selects the billboard slots from the available ones in an incremental greedy manner, and we call this method the Budget Effective Greedy approach. In the second one, we introduce randomness in the first one, where we do it for a sample of slots instead of calculating the marginal gains of all the billboard slots. We analyze both algorithms to understand their time and space complexity. We implement them with real-life datasets and conduct a number of experiments. We observe that the randomized budget effective greedy approach takes reasonable computational time while minimizing the regret.

Problem

• Minimizing advertiser regret in billboard ad allocation
• Optimizing slot assignment to reduce influence provider losses
• Developing greedy algorithms for efficient regret minimization

Innovation

• Incremental greedy billboard slot selection
• Randomized sampling for reduced computation
• Approximately bisubmodular regret minimization framework