CAREER: Learning Theory for Large-scale Stochastic Games

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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.