Abstract
In this paper, we consider to learn the inherent probability distribution of types via knowledge transfer in a two-player repeated Bayesian game, which is a basic model in network security. In the Bayesian game, the attacker’s distribution of types is unknown by the defender and the defender aims to reconstruct the distribution with historical actions. It is difficult to calculate the distribution of types directly since the distribution is coupled with a prediction function of the attacker in the game model. Thus, we seek help from an interrelated complete-information game, based on the idea of transfer learning. We provide two different methods to estimate the prediction function in different concrete conditions with knowledge transfer. After obtaining the estimated prediction function, the defender can decouple the inherent distribution and the prediction function in the Bayesian game, and moreover, reconstruct the distribution of the attacker’s types. Finally, we give numerical examples to illustrate the effectiveness of our methods.
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The authors would like to thank Prof. Peng Yi for his helpful suggestions.
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This work was supported by the National Key Research and Development Program (No. 2016YFB0901900) and the National Natural Science Foundation of China (No. 61733018).
Guanpu CHEN received the B.Sc. degree in Mathematics and Applied Mathematics from University of Science and Technology of China, Hefei, China, in 2017. He is currently a Ph.D. candidate in Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China. His research interests include game theory, distributed optimization and transfer learning.
Kai CAO received the B.E. degree from University of Science and Technology of China in 2017. He is currently working towards the Ph.D. degree in Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests include transfer learning, big data analysis and biocomputing.
Yiguang HONG received his B.Sc. and M.Sc. degrees from Peking University, China, and the Ph.D. degree from the Chinese Academy of Sciences (CAS), China. He is currently a Professor in Academy of Mathematics and Systems Science, CAS. His current research interests include nonlinear control, multiagent systems, distributed optimization/ game, machine learning, and social networks. Prof. Hong serves as Editor-in-Chief of Control Theory and Technology. He also serves or served as Associate Editors for many journals including the IEEE Transactions on Automatic Control, IEEE Transactions on Control of Network Systems, and IEEE Control Systems Magazine. He is a recipient of the Guang Zhaozhi Award at the Chinese Control Conference, Young Author Prize of the IFAC World Congress, Young Scientist Award of CAS, the Youth Award for Science and Technology of China, and the National Natural Science Prize of China. He is also a Fellow of IEEE.
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Chen, G., Cao, K. & Hong, Y. Learning implicit information in Bayesian games with knowledge transfer. Control Theory Technol. 18, 315–323 (2020). https://doi.org/10.1007/s11768-020-0086-2
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DOI: https://doi.org/10.1007/s11768-020-0086-2