We study the problem of minimizing regret in multi-mode advertisement settings, where an influence provider allocates advertising resources such as social network seeds and billboard slots to multiple advertisers with specified influence demands and payments. Unlike prior work focusing on a single mode of advertising, we consider the interplay between online and offline modes and introduce a novel regret model that captures their interaction effect. This leads to a regret minimization problem that is non-monotone, non-submodular, and NP-hard to approximate within any constant factor. To address this, we propose a monotone, approximately bisubmodular influence model and develop two algorithmic solutions: Projected Subgradient Method based on the Lovász extension of the regret function, and an Approximate Bisubmodular Local Search algorithm with provable guarantees. Experiments on large-scale real-world datasets, including billboard and trajectory data from major U.S. cities, as well as social network graphs, demonstrate that our methods outperform existing baselines in minimizing total regret while satisfying advertiser demands. Our framework is broadly applicable to other resource allocation scenarios beyond advertising.

翻译：我们研究了多模式广告场景中的遗憾最小化问题，其中影响力提供者将社交媒体种子用户和广告牌时段等广告资源分配给多个广告商，这些广告商具有特定的影响力需求和支付预算。与先前专注于单一广告模式的研究不同，我们考虑了线上与线下模式之间的相互作用，并引入了一种新的遗憾模型来捕捉它们的交互效应。这导致了一个非单调、非次模且无法在任意常数因子内近似求解的NP难遗憾最小化问题。为解决此问题，我们提出了一种单调的近似双次模影响力模型，并开发了两种算法解决方案：基于遗憾函数Lovász扩展的投影次梯度方法，以及具有可证明保证的近似双次模局部搜索算法。在大规模真实数据集上的实验，包括来自美国主要城市的广告牌与轨迹数据以及社交网络图，表明我们的方法在满足广告商需求的同时，在最小化总遗憾方面优于现有基线。我们的框架广泛适用于广告之外的其他资源分配场景。