Seminars

Home Centers & Programs AI and Natural Sciences Seminars

TITLE: Solving Nonconvex Hamilton--Jacobi--Isaacs Equations with PINN--Based Policy Iteration

ABSTRACT: We present a mesh-free policy iteration framework that integrates classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic differential games and robust control. The method alternates between solving linear second-order PDEs under fixed feedback policies and updating controls via pointwise minimax optimization with automatic differentiation. Under standard Lipschitz continuity and uniform ellipticity assumptions, we establish convergence of the value function iterates to the unique viscosity solution, supported by an equi-Lipschitz regularity analysis. Numerical experiments validate the accuracy and scalability of the approach: in two-dimensional stochastic path-planning games, the method achieves relative $L^2$-errors below $10^{-2}$, while in five- and ten-dimensional publisher–subscriber games, it consistently outperforms direct PINN solvers, producing smoother value functions and lower residuals. These results demonstrate that combining PINNs with policy iteration provides a practical and theoretically grounded framework for solving high-dimensional, nonconvex HJI equations, with applications in robotics, finance, and multi-agent reinforcement learning. This work is jointly done with HJ Yang and M. Gim (NIMS).