  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.
