Infer Your Enemies and Know Yourself, Learning in Real-Time Bidding with Partially Observable Opponents

Abstract

Real-time bidding, as one of the most popular mechanisms for selling online ad slots, facilitates advertisers to reach their potential customers. The goal of bidding optimization is to maximize the advertisers' return on investment (ROI) under a certain budget setting. A straightforward solution is to model the bidding function in an explicit form. However, the static functional solutions lack generality in practice and are insensitive to the stochastic behaviour of other bidders in the environment. In this paper, we propose a general multi-agent framework with actor-critic solutions facing against playing imperfect information games. We firstly introduce a novel Deep Attentive Survival Analysis (DASA) model to infer the censored data in the second price auctions which outperforms start-of-the-art survival analysis. Furthermore, our approach introduces the DASA model as the opponent model into the policy learning process for each agent and develop a mean field equilibrium analysis of the second price auctions. The experiments have shown that with the inference of the market, the market converges to the equilibrium much faster while playing against both fixed strategy agents and dynamic learning agents.