The National Science Foundation (NSF) Computer and Information Science and Engineering program (CFDA 47.070) awarded $249,987 to the University of California, Berkeley on July 1, 2025, to conduct collaborative research on building a mathematical foundation for deep reinforcement learning (DRL). This project addresses a critical gap in theoretical understanding of DRL systems, which have achieved significant real-world breakthroughs in robotics, gaming, healthcare, and transportation but lack adequate mathematical frameworks to explain their empirical success. The research will leverage tools from approximation theory, control theory, and optimization theory to systematically characterize the computational and statistical complexity of DRL, enabling the design of more efficient and reliable empirical methods for neural network-based sequential decision-making systems.
The project comprises three primary research thrusts: identifying achievable performance guarantees for different reinforcement learning problem instances using non-convex optimization tools; investigating neural network complexity and capacity control through approximation theory; and developing practical implications for DRL algorithm design. Complementing the research activities, the award supports comprehensive education and outreach initiatives, including mentorship of graduate and undergraduate students (particularly through programs serving underrepresented groups), development of new courses and monographs, organization of research workshops, and creation of high school curriculum materials in data science and artificial intelligence. The project is scheduled for completion by September 30, 2026.