Today, billions of display ad impressions are purchased on a daily basis through a public auction hosted by real time bidding (RTB) exchanges. A decision has to be made for advertisers to submit a bid for each selected RTB ad request in milliseconds. Restricted by the budget, the goal is to buy a set of ad impressions to reach as many targeted users as possible. A desired action (conversion), advertiser specific, includes purchasing a product, filling out a form, signing up for emails, etc. In addition, advertisers typically prefer to spend their budget smoothly over the time in order to reach a wider range of audience accessible throughout a day and have a sustainable impact. However, since the conversions occur rarely and the occurrence feedback is normally delayed, it is very challenging to achieve both budget and performance goals at the same time. In this paper, we present an online approach to the smooth budget delivery while optimizing for the conversion performance. Our algorithm tries to select high quality impressions and adjust the bid price based on the prior performance distribution in an adaptive manner by distributing the budget optimally across time. Our experimental results from real advertising campaigns demonstrate the effectiveness of our proposed approach.
Agrawal @cite_9 proposed an general online linear programming algorithm to solve many practical online problems. First they applied the standard linear programming solver to compute the optimal dual solution for the data which have been seen in the system. Then, the solution for the new instance can be decided by checking if the dual solution with the new instance satisfies the constraint. The problem is that the true value @math and cost @math for the incoming ad request is unknown when it arrives to the system. If @math and @math is estimated by some statistical models or other alternative solutions, the dual solution needs to be re-computed more frequently for each campaign in order to impose budget constraints accurately. This introduces high computational cost in the real time bidding system.
@cite_9
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A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding objective coefficient. In such a model, a decision variable has to be set each time a column is revealed without observing the future inputs and the goal is to maximize the overall objective function. In this paper, we provide a near-optimal algorithm for this general class of online problems under the assumption of random order of arrival and some mild conditions on the size of the LP right-hand-side input. Specifically, our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from the revealed columns in the previous period are used to determine the sequential decisions in the current period. Due to the feature of dynamic learning, the competitiveness of our algorithm improves over the past study of the same problem. We also present a worst-case example showing that the performance of our algorithm is near-optimal.