  In this paper, we consider the problem of optimizing the revenue a web
publisher gets through real-time bidding (i.e. from ads sold in real-time
auctions) and direct (i.e. from ads sold through contracts agreed in advance).
We consider a setting where the publisher is able to bid in the real-time
bidding auction for each impression. If it wins the auction, it chooses a
direct campaign to deliver and displays the corresponding ad.
  This paper presents an algorithm to build an optimal strategy for the
publisher to deliver its direct campaigns while maximizing its real-time
bidding revenue. The optimal strategy gives a formula to determine the
publisher bid as well as a way to choose the direct campaign being delivered if
the publisher bidder wins the auction, depending on the impression
characteristics.
  The optimal strategy can be estimated on past auctions data. The algorithm
scales with the number of campaigns and the size of the dataset. This is a very
important feature, as in practice a publisher may have thousands of active
direct campaigns at the same time and would like to estimate an optimal
strategy on billions of auctions.
  The algorithm is a key component of a system which is being developed, and
which will be deployed on thousands of web publishers worldwide, helping them
to serve efficiently billions of ads a day to hundreds of millions of visitors.
