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，决策已演变为多方面的过程，涉及各个方面，例如人口异质性，潜水员信息结构和人类互动。该项目旨在开发新的学习框架和数学基础，以增强我们对人口众多社会系统的稳定，效率和公平性的理解。这项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，并适应异构风险偏好以及信息不对称。这项研究将涉及本科和研究生，强调数学和机器学习方面的跨学科培训。此外，还将建立一个外展计划，以使代表性不足的群体参与STEM。该项目的核心位置是随机系统的机器学习理论的数学进步，其中许多相互作用的代理，称为“平均场景游戏”。第一个目标是在结构性属性（例如Graphon Itsvortitions或人口分布的其他摘要统计数据）下，为平均场游戏开发新的数学模型和学习算法。这种发展取决于基于流的局部传播的新近似方案和稳定性分析。第二个目标的重点是主要代理问题，在该问题中，代理具有潜水员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，从而导致了一类新型的随机部分微分方程，这些方程需要新的开发方案，以实现明确的定义性和规律性理论。最终目标的重点是用交互式平均场代理构建通用模型（模拟器），以解决基于代理的模拟器文献中的可伸缩性问题。为了利用神经元网络的计算能力，一个关键目标是在分布意义上建立通用近似定理，并建立迭代深度学习计划的融合来培训模拟器。该奖项反映了NSF的法定任务，并通过使用该基金会的智力功能和广泛的影响来评估NSF的法定任务，并被认为是珍贵的支持。