Bid optimization for online advertising from single advertiser's perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose. (2) Previous works cannot well handle the underlying complex bidding environment, leading to poor model convergence. This problem could be amplified when handling multiple objectives of advertisers which are practical demands but not considered by previous work. In this paper, we propose a novel multi-objective cooperative bid optimization formulation called Multi-Agent Cooperative bidding Games (MACG). MACG sets up a carefully designed multi-objective optimization framework where different objectives of advertisers are incorporated. A global objective to maximize the overall profit of all advertisements is added in order to encourage better cooperation and also to protect self-bidding advertisers. To avoid collusion, we also introduce an extra platform revenue constraint. We analyze the optimal functional form of the bidding formula theoretically and design a policy network accordingly to generate auction-level bids. Then we design an efficient multi-agent evolutionary strategy for model optimization. Evolutionary strategy does not need to model the underlying environment explicitly and is more suitable for bid optimization. Offline experiments and online A/B tests conducted on the Taobao platform indicate both single advertiser's objective and global profit have been significantly improved compared to state-of-art methods.

Multi-view clustering aims to leverage information from multiple views to improve clustering. Most previous works assumed that each view has complete data. However, in real-world datasets, it is often the case that a view may contain some missing data, resulting in the incomplete multi-view clustering problem. Previous methods for this problem have at least one of the following drawbacks: (1) employing shallow models, which cannot well handle the dependence and discrepancy among different views; (2) ignoring the hidden information of the missing data; (3) dedicated to the two-view case. To eliminate all these drawbacks, in this work we present an Adversarial Incomplete Multi-view Clustering (AIMC) method. Unlike most existing methods which only learn a new representation with existing views, AIMC seeks the common latent space of multi-view data and performs missing data inference simultaneously. In particular, the element-wise reconstruction and the generative adversarial network (GAN) are integrated to infer the missing data. They aim to capture overall structure and get a deeper semantic understanding respectively. Moreover, an aligned clustering loss is designed to obtain a better clustering structure. Experiments conducted on three datasets show that AIMC performs well and outperforms baseline methods.

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