Yield optimization of display advertising with ad exchange

In light of the growing market of Ad Exchanges for the real-time sale of advertising slots, publishers face new challenges in choosing between the allocation of contract-based reservation ads and spot market ads. In this setting, the publisher should take into account the tradeoff between short-term revenue from an Ad Exchange and quality of allocating reservation ads. In this paper, we formalize this combined optimization problem as a stochastic control problem and derive an efficient policy for online ad allocation in settings with general joint distribution over placement quality and exchange bids. Ad Exchanges like RightMedia, AdECN or DoubleClick are an emerging market for the real-time sale of display advertising slots in publishing sites on the Internet. While exchanges differ in their implementations, in a generic Ad Exchange (AdX), publishers post an ad slot with a reservation price, advertisers post bids, and an auction is run; this happens between the time a user visits a page and the ad is displayed.
 From the publisher's point of view, the goal is to maximize revenue gained from sale of the ad inventory. In isolation, this problem is similar to optimal auction design, and Myerson shows that the optimal reserve price can be calculated from the bid distribution. However, AdX represents only one possible sales outlet for the publisher. In fact, even in the presence of this efficient real-time market, many web publishers still get a significant portion of their revenue from making individual deals with specific advertisers or agencies. These deals usually take the form of a specific number of ad impressions reserved over a particular time horizon (e.g., one million impressions over a month). A publisher can make many such deals with different advertisers, with potentially sophisticated relationships between the advertisers' targeting criteria. So for a given piece of ad inventory, the publisher must decide---quickly---whether to send the inventory to AdX (and at what price), or to assign it to an advertiser with a reservation.
 In this paper, we study the problem faced by the publisher, jointly optimizing over AdX and the reservations. We bring to bear techniques from revenue management and stochastic optimization, and derive an efficient policy for making real-time ad allocation decisions. We prove that our policy is asymptotically optimal in terms of an arbitrary (i.e., publisher-defined) trade-off between quality delivered to reservation ads and revenue from the exchange. Our policy and analysis is quite general, and works for any joint distribution over placement quality and exchange bids, even allowing correlation between advertisers, or between quality and exchange bids. In particular, we provide a rigorous bound on the convergence rate of our policy to the optimal policy. We also give experimental results on data derived from real publisher inventory, showing that our policy lets us achieve any pareto-optimal point on the quality vs. revenue curve.
 Finally, we study a parametric training-based algorithm in which instead of learning the dual variables from a sample data (as is done in non-parametric training-based algorithms), we learn the parameters of the distribution and construct those dual variables from the learned parameter values. We compare parametric and non-parametric ways to estimate from data both analytically and experimentally in the special case without the ad exchange, and show that though both methods converge to the optimal policy as the sample size grows, our parametric method converges faster, and thus performs better on smaller samples.