Learning to Price against a Budget and ROI Constrained Buyer

TL;DR

This paper develops a seller pricing algorithm in repeated ad auctions that learns to maximize revenue against a buyer constrained by budget and ROI, using a binary-search approach with low regret.

Contribution

It introduces a novel episodic binary-search algorithm for sellers to learn revenue-optimal prices in a constrained buyer setting, with provably low regret.

Findings

The seller's revenue function has a bell-shaped structure under buyer best responses.

The proposed algorithm efficiently identifies near-optimal prices with low regret.

Buyer algorithms satisfying constraints lead to stable, approximately best responding behavior.

Abstract

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.