Optimal real-time bidding for display advertising

In this paper we study bid optimisation for real-time bidding (RTB) based display advertising. RTB allows advertisers to bid on a display ad impression in real time when it is being generated. It goes beyond contextual advertising by motivating the bidding focused on user data and it is different from the sponsored search auction where the bid price is associated with keywords. For the demand side, a fundamental technical challenge is to automate the bidding process based on the budget, the campaign objective and various information gathered in runtime and in history. In this paper, the programmatic bidding is cast as a functional optimisation problem. Under certain dependency assumptions, we derive simple bidding functions that can be calculated in real time; our finding shows that the optimal bid has a non-linear relationship with the impression level evaluation such as the click-through rate and the conversion rate, which are estimated in real time from the impression level features. This is different from previous work that is mainly focused on a linear bidding function. Our mathematical derivation suggests that optimal bidding strategies should try to bid more impressions rather than focus on a small set of high valued impressions because according to the current RTB market data, compared to the higher evaluated impressions, the lower evaluated ones are more cost effective and the chances of winning them are relatively higher. Aside from the theoretical insights, offline experiments on a real dataset and online experiments on a production RTB system verify the effectiveness of our proposed optimal bidding strategies and the functional optimisation framework.