In digital online advertising, advertisers procure ad impressions simultaneously on multiple platforms, or so-called channels, such as Google Ads, Meta Ads Manager, etc., each of which consists of numerous ad auctions. We study how an advertiser maximizes total conversion (e.g. ad clicks) while satisfying aggregate return-on-investment (ROI) and budget constraints across all channels. In practice, an advertiser does not have control over, and thus cannot globally optimize, which individual ad auctions she participates in for each channel, and instead authorizes a channel to procure impressions on her behalf: the advertiser can only utilize two levers on each channel, namely setting a per-channel budget and per-channel target ROI. In this work, we first analyze the effectiveness of each of these levers for solving the advertiser's global multi-channel problem. We show that when an advertiser only optimizes over per-channel ROIs, her total conversion can be arbitrarily worse than what she could have obtained in the global problem. Further, we show that the advertiser can achieve the global optimal conversion when she only optimizes over per-channel budgets. In light of this finding, under a bandit feedback setting that mimics real-world scenarios where advertisers have limited information on ad auctions in each channels and how channels procure ads, we present an efficient learning algorithm that produces per-channel budgets whose resulting conversion approximates that of the global optimal problem. Finally, we argue that all our results hold for both single-item and multi-item auctions from which channels procure impressions on advertisers' behalf.

翻译：在数字在线广告领域，广告主需同时在多个平台（即所谓的渠道，例如Google Ads、Meta Ads Manager等）上采购广告曝光机会，每个渠道均包含大量广告拍卖。本文研究广告主如何在满足跨渠道总投资回报率（ROI）与总预算约束的前提下，最大化总转化量（如广告点击量）。实践中，广告主无法控制也无力全局优化其参与各渠道中具体广告拍卖的行为，转而授权各渠道代其采购广告曝光机会：广告主仅能针对每个渠道设置两个调节杠杆，即单渠道预算与单渠道目标ROI。本文首先分析各杠杆在解决广告主全局多渠道问题中的有效性。研究表明，当广告主仅优化各渠道ROI时，其总转化量可能任意劣于全局优化方案的理论最优值。进一步地，当广告主仅优化各渠道预算时，其总转化量可达到全局最优值。基于此发现，在模拟现实场景（广告主对各渠道广告拍卖信息及渠道广告采购机制认知有限）的bandit反馈设定下，我们提出一种高效学习算法，能够生成各渠道预算，使得实际转化量逼近全局最优解。最后，我们论证所有结论在渠道代广告主采购广告曝光机会的单物品拍卖与多物品拍卖场景中均成立。