مقایسه قیمت های پیش بینی شده در مزایده ها برای تبلیغات آنلاین

Online publishers sell opportunities to show ads. Some advertisers pay only if their ad elicits a user response. Publishers estimate response rates for ads in order to estimate expected revenues from showing the ads. Then publishers select ads that maximize estimated expected revenue. By taking a maximum among estimates, publishers inadvertently select ads based on a combination of actual expected revenue and inaccurate estimation of expected revenue. Publishers can increase actual expected revenue by selecting ads to maximize a combination of estimated expected revenue and estimation accuracy.

Online publishers use auctions to sell opportunities to advertise, called ad calls, to online advertisers. There are two broad categories of online advertising auctions: search and display. In search advertising auctions the advertiser pays only if their ad elicits a click. In display advertising auctions, advertisers may select a basis for payment. Some advertisers pay when the ad is shown, others pay only when showing the ad elicits a user response such as a click or a purchase. (For details on auctions for online advertising, refer to Varian, 2006, Varian, 2009, Edelman et al., 2007 and Lahaie and Pennock, 2007.) When advertisers pay per click or other user response, the revenue received by the publisher for showing an ad is random. Since user response rates are not known exactly but must be estimated, there is uncertainty in addition to randomness. The estimation accuracy of response rates varies. One reason is that the amount of historical data varies. Another reason is that the response rates themselves vary, and more data is required to estimate smaller rates with the same relative accuracy. With randomness, a risk-neutral seller seeks to maximize expected revenue. Facing uncertainty, the seller may select an offer having maximum estimated expected revenue. However, this is not necessarily the best policy for maximizing actual expected revenue.

This paper explores the impact of using estimates of offer values in an auction. Using estimates introduces a bias that can significantly reduce revenue and selectivity. This paper also outlines a method to correct for the bias, improving revenue and selectivity. The method selects an auction winner based on a combination of estimated offer value and an estimate of the estimation error. The method in this paper has free parameters. To apply the method in practice, it is possible to use simulations to select starting points for the parameters. Then use statistical optimization techniques, as in Box et al. (2005) to adjust the parameters, optimizing for any desired combination of revenue and selectivity. Fortunately, the simulations in this paper indicate that revenue-optimal parameter settings are similar to selectivity-optimal ones. Our simulations showed that optimal values of c depend on the number of offers in each auction. This is similar to classical shrinkage methods such as James–Stein estimation ( James and Stein, 1961 and Stein, 1955). Most shrinkage methods are designed to minimize average error over the quantities being estimated; see for example Brown, 1966 and Bock, 1975. For auctions with a single winner, it would be interesting to explore whether there are estimators that tend to select the offer with highest actual mean directly, rather than first applying shrinkage methods and then selecting the maximum estimate. In practice, many auctions contain some offers that are not competitive. Those offers should be removed before applying corrections or shrinkage. Uncompetitive offers can be identified using uniform error bound methods from machine learning, such as Hoeffding (1963) bounds or Audibert et al.'s empirical Bernstein (Audibert et al., 2007 and Mnih et al., 2008) bounds. Offers with upper bounds on value less than the maximum offer value lower bound can be declared uncompetitive and removed.