Data-Driven optimal control via Koopman operators and Hamilton-Jacobi-Bellman equations

What the math gives to ML

The paper combines Koopman-generator identification with geometric solution of Hamilton-Jacobi-Bellman equations, offering a structured way to learn controlled dynamics and value functions from trajectories. The transferable asset is the generator identity: derivatives of observables along trajectories become a differentiable, data-estimable representation of the vector field and control directions. A practical neural adaptation is to learn a control-affine latent lift and train a value network with an HJB residual computed through that learned generator, producing feedback directly from the value gradient. This may improve data efficiency and closed-loop stability relative to an unconstrained actor-critic, especially in low-dimensional continuous control.