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：在数字在线广告中，广告主同时在多个平台（即所谓通道，如Google Ads、Meta Ads Manager等）上采购广告展示机会，每个平台包含众多广告拍卖。我们研究广告主如何在满足所有通道的总投资回报率（ROI）与预算约束下，最大化总转化量（如广告点击次数）。实际中，广告主无法控制每个通道参与的具体广告拍卖，因而不能进行全局优化，而是授权通道代其采购展示机会：广告主仅能对每个通道使用两个杠杆，即设置通道预算与通道目标ROI。本文首先分析每个杠杆在解决广告主全局多通道问题中的有效性。我们证明，当广告主仅优化各通道ROI时，其总转化量可能任意劣于全局问题所能取得的最优值。进一步，我们证明广告主仅优化各通道预算即可实现全局最优转化。基于此发现，在模拟现实场景的带状反馈设定下（广告主对各通道的广告拍卖及通道采购方式信息有限），我们提出一种高效学习算法，其产生的通道预算对应的转化量逼近全局最优问题。最后，我们论证所有结论在单物品与多物品拍卖中均成立——这些拍卖正是通道代广告主采购展示机会的方式。