Internet advertisers (buyers) repeatedly procure ad impressions from ad platforms (sellers) with the aim to maximize total conversion (i.e. ad value) while respecting both budget and return-on-investment (ROI) constraints for efficient utilization of limited monetary resources. Facing such a constrained buyer who aims to learn her optimal strategy to acquire impressions, we study from a seller's perspective how to learn and price ad impressions through repeated posted price mechanisms to maximize revenue. For this two-sided learning setup, we propose a learning algorithm for the seller that utilizes an episodic binary-search procedure to identify a revenue-optimal selling price. We show that such a simple learning algorithm enjoys low seller regret when within each episode, the budget and ROI constrained buyer approximately best responds to the posted price. We present simple yet natural buyer's bidding algorithms under which the buyer approximately best responds while satisfying budget and ROI constraints, leading to a low regret for our proposed seller pricing algorithm. The design of our seller algorithm is motivated by the fact that the seller's revenue function admits a bell-shaped structure when the buyer best responds to prices under budget and ROI constraints, enabling our seller algorithm to identify revenue-optimal selling prices efficiently.

翻译：互联网广告主（买方）为高效利用有限资金，需在满足预算与投资回报率（ROI）双重约束的前提下，从广告平台（卖方）反复购买广告展示机会以最大化总转化价值（即广告价值）。面对此类试图学习最优竞价策略的受约束买方，我们从卖方视角研究如何通过重复报价机制学习并确定广告展示价格，以实现收益最大化。针对这种双边学习场景，我们提出一种基于分阶段二分搜索的卖方学习算法，通过识别收益最优的销售价格。理论分析表明：当每阶段内受预算与ROI约束的买方对报价做出近似最优响应时，该简单学习算法可实现较低的卖方遗憾值。我们进一步提出自然且简明的买方竞价算法，该算法可在满足预算与ROI约束的条件下生成近似最优响应，从而保证所提卖方定价算法的低遗憾特性。卖方算法的设计源于关键发现：当买方在预算与ROI约束下对价格做出最优响应时，卖方收益函数呈现钟形结构，这使得卖方算法能够高效识别收益最优的销售价格。