JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (1): 1-10, 45.doi: 10.6040/j.issn.1671-9352.0.2023.512

• Invited Review •     Next Articles

Strategic limit theory and strategic statistical learning

Xiaodong YAN()   

  1. Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, Shandong, China
  • Received:2023-12-05 Online:2024-01-20 Published:2024-01-19

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Abstract:

The nonlinear expectation is an original research direction pioneered by Academician Peng Shige of Shandong University, which is becoming increasingly important in various fields of scientific research. The rise of big data and artificial intelligence has provided stronger impetus for innovative theoretical and applied research in nonlinear expectation. Recently, Shandong University's Nonlinear Probability Team has developed the "Strategy Limit Theory" based on the strategic game process of multi-armed bandits, representing a significant breakthrough in the intersection of nonlinear probability theory and reinforcement learning. This has tran-sformed the research paradigm of traditional statistical methods. Based on the proposed 10 basic mathematical problems of artificial intelligence by Academician Xu Zongben, the declaration guide of 2022 major research plan projects issued by the National Natural Science Foundation of China for the research about universal and interpretable artificial intelligence technologies, and the application guide for basic mathematical theory research of artificial intelligence in 2021 and 2022 the key projects of "Mathematics and Applied Research" issued by the Ministry of Science and Technology, this article adopts the concept of "strategy" to reveal the nature of artificial intelligence and explore and the motivation source and theoretical basis for initiating and promoting the innovation of artificial intelligence technology. Different from the applications of the traditional law of large numbers and the central limit theorem in the field of artificial intelligence, we propose novel theory about the strategic law of large numbers and the central limit theorem in the new generation of artificial intelligence. The discussed topics in this work include but not limited to: (1) strategic sampling of massive data; (2) online learning of streaming data; (3) the central limit theorem of reinforcement learning; (4) differential privacy protection of data; (5) strategic integration of federal learning; (6) information reconstruction of transfer learning and meta learning; (7) the fusion of knowledge reasoning and data driving.

Key words: artificial intelligence, strategic limit theory, mathematical foundation, big data analysis, reinforcement learning, online learning, transfer learning, federated learning, data privacy protection, knowledge reasoning and data driving

CLC Number: 

  • TP18

Fig.1

Different probability density functions of the peak distribution f(z) and the binormal distribution g(z) as the parameters k, h change, where the green line is the probability density function plot of the standard normal distribution"

Fig.2

Coverage probability of the 3 peak distribution probability density functions Xt(blue), Yt (green), and R0, Π* (red) in the interval [a, b], where the expectations of Xt and Xt are set to μL=-1, μR=1 and the variances are set to σL=σR=1, respectively, and consider the three intervals[0, 1], [0.5, 1.5], [1, 2]"

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