策略极限理论与策略统计学习

doi:10.6040/j.issn.1671-9352.0.2023.512

摘要/Abstract

摘要：

非线性期望是山东大学彭实戈院士开辟的原创性研究方向之一, 对各个领域的科学研究越来越重要, 而大数据和人工智能的兴起, 为非线性期望创新理论与应用研究提供了更强劲的动力。最近, 山东大学“非线性期望”团队基于多臂老虎机的策略博弈过程开创了“策略极限理论”, 是非线性概率理论与强化学习交叉的重大突破性科研成果, 变革了传统统计方法研究范式。本文结合徐宗本院士提出的人工智能的10个重大数理基础问题, 国家自然科学基金委员会发布的2022年度重大研究计划项目中关于可解释、可通用的人工智能方法的申报指南, 以及科技部发布的数学和应用研究重点专项2021、2022年度项目中“数据科学与人工智能的数学基础”理论研究的申报指南, 采用“策略”这一概念探寻和揭示人工智能本质和规律, 尝试启发、促动人工智能技术变革的激发源和理论依据。不同于传统的大数定律和中心极限定理在独立同分布假设下开展统计学习的研究, 策略极限理论打破了数据可交换这一局限, 在更大的概率空间中探求最优分布, 并提出获得最优分布的最优策略路径, 与之对应的统计学习过程被命名为策略统计学习, 为复杂机器学习的可解释和可信赖的统计方法研究提供理论支撑。本文介绍策略极限理论的应用包括但不限于: (1)大规模数据的策略抽样; (2)数据流的在线学习; (3)强化学习的中心极限定理; (4)数据的差分隐私保护; (5)联邦学习的策略融合; (6)迁移学习和元学习的信息重构; (7)知识推理与数据驱动的融合。

关键词: 人工智能, 策略极限理论, 数理基础, 大数据分析, 强化学习, 在线学习, 迁移学习, 联邦学习, 数据隐私保护, 知识推理与数据驱动

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

中图分类号:

TP18

严晓东. 策略极限理论与策略统计学习[J]. 《山东大学学报(理学版)》, 2024, 59(1): 1-10, 45.

Xiaodong YAN. Strategic limit theory and strategic statistical learning[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(1): 1-10, 45.

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