Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

Understand

We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models.

• The algorithm continuously updates the SDE model's parameters using an estimate for the gradient of the stationary distribution.
• The gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, asymptotically converging to the direction of steepest descent.
• We rigorously prove convergence of the online forward propagation algorithm for linear SDE models (i.e., the multi-dimensional Ornstein-Uhlenbeck process) and present its numerical results for nonlinear examples.