Hamilton-Jacobi-Bellman Equation: Reinforcement Learning and Diffusion Models
Machine learning feels recent, but one of its core mathematical ideas dates back to 1952, when Richard Bellman published a seminal paper titled “On the Theory of Dynamic Programming” [6, 7], laying the foundation for optimal control and what we now call reinforcement learning. Later in the 50s, Bellman extended his work to continuous-time systems, turning the optimal condition into a PDE. What he later found was that this was identical to a result in physics published a century before (1840s), known as the Hamilton-Jacobi equation. ...