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，如谷歌广告、元广告管理器等）上采购广告展示机会，每个通道均包含大量广告拍卖。我们研究广告主如何在满足所有通道总体投资回报率与预算约束的同时，最大化总转化量（如广告点击）。实际中，广告主无法控制每个通道参与的特定广告拍卖，因而无法进行全局优化；相反，广告主授权通道代表其采购展示机会：广告主只能为每个通道使用两种杠杆，即设定单通道预算与单通道目标投资回报率。本文首先分析这些杠杆在解决广告主全局多通道问题中的有效性。我们证明，当广告主仅优化单通道投资回报率时，其总转化量可能比全局问题中能获得的结果任意差。进一步，我们证明当广告主仅优化单通道预算时，可以达到全局最优转化量。基于这一发现，在模拟现实场景的强盗反馈设置下（广告主对各通道广告拍卖信息及通道广告采购方式了解有限），我们提出一种高效学习算法，其生成的单通道预算使得最终转化量逼近全局最优问题的结果。最后，我们论证所有结论对单物品拍卖与多物品拍卖均成立，这些拍卖是通道代表广告主采购展示机会的方式。