CAREER: Learning Theory for Large-scale Stochastic Games

职业：大规模随机博弈的学习理论

• 批准号: 2339240
• 负责人: Renyuan Xu
• 金额: $ 40.96万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-02-01 至 2029-01-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2339240&HistoricalAwards=false
• 关键词: CAREER; Learning; Theory; Large; scale

In modern financial markets and economic systems with large populations, decision-making has evolved into a multifaceted process involving various aspects such as population heterogeneity, diverse information structures, and human-AI interactions. This project aims to develop new learning frameworks and mathematical foundations that strengthen our understanding of the stability, efficiency, and fairness of societal systems with large populations. Novel frameworks developed in this research are designed to have flexible model assumptions, be able to learn from incomplete information, and accommodate heterogeneous risk preferences as well as information asymmetry. This research will involve both undergraduate and graduate students, emphasizing cross-disciplinary training in mathematics and machine learning. Additionally, an outreach program will be established to engage underrepresented groups in STEM.This project places at its core the mathematical advancement of machine learning theory for stochastic systems with many interacting agents, known as “mean-field games”. The first goal is to develop new mathematical models and learning algorithms for mean-field games under structural properties such as graphon interactions or additional summary statistics of the population distribution. This development relies on new approximation schemes and stability analyses based on the local propagation of flows. The second goal focuses on principal-agent problems, where agents have diverse risk preferences or the capability to acquire new information. These topics pose significant challenges in a dynamic setting, leading to a novel class of stochastic partial differential equations that require new developments for well-definedness and regularity theory. The final goal focuses on constructing generative models (simulators) with interactive mean-field agents, addressing the scalability issue in agent-based simulator literature. To leverage the computational power of neural networks, a key objective is to establish a universal approximation theorem in the distributional sense and the convergence of an iterative deep-learning scheme to train the simulator.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在人口众多的现代金融市场和经济体系中，决策已演变成一个多方面的过程，涉及人口异质性、多样化的信息结构和人机交互等各个方面。该项目旨在开发新的学习框架和数学基础。加强我们对人口众多的社会系统的稳定性、效率和公平性的理解。本研究中开发的新框架旨在具有灵活的模型假设，能够从不完整的信息中学习，并适应异质风险偏好和信息不对称。 .这项研究将涉及本科生和研究生，强调数学和机器学习的跨学科培训。此外，还将建立一个外展计划，以吸引 STEM 中代表性不足的群体。该项目的核心是随机系统的机器学习理论的数学进步。交互代理，称为“平均场博弈”，第一个目标是在图子交互或人口分布的附加汇总统计等结构特性下开发新的平均场博弈数学模型和学习算法。近似方案和稳定性基于流量的局部传播的分析侧重于委托代理问题，其中代理具有不同的风险偏好或获取新信息的能力，这些主题在动态环境中提出了重大挑战，导致了一种新型的随机问题。偏微分方程需要明确定义和规律性理论的新发展，最终目标侧重于利用交互式平均场代理构建生成模型（模拟器），解决基于代理的模拟器文献中的可扩展性问题。神经网络，一个关键目标是建立分布意义上的通用逼近定理和迭代深度学习方案的收敛来训练模拟器。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和能力进行评估，被认为值得支持。更广泛的影响审查标准。