Optimal Bidding Strategy with Smooth Budget Delivery in Online Advertising

In this paper, the optimal bidding strategy with smooth budget delivery in a real-time bidding (RTB) platform is addressed. Feedback control theory plays an essential role in the performance enhancement of ad campaigns in online advertising industry. The objective is to determine the optimal bidding prices as control signals such that (i) the total number of clicks by visiting users is maximized, and (ii) the campaign budget in every episode is smoothly delivered without a premature finishing of the campaign budget or excessive spending rates. In this paper, the advertisers are regarded as the agents in a Markov decision process, where the rewards are chosen according to the main campaign objectives. An advertiser is supposed to select a sequence of bidding actions in terms of a control policy such that a long-term accumulation of the rewards is maximized. It is shown that the smooth bidding with real-time adaptation fits into the framework of reinforcement learning with dynamic programming. Accordingly, an approximation algorithm is proposed to solve the corresponding Bellman optimality equation. The results are utilized to form the bidding strategy with smooth budget delivery. Simulation results on a real-world dataset confirm that the proposed approach outperforms the state-of-the-art bidding strategies, by sustainable participation in the auctions, and maximizing the number of user clicks.