In this talk, I'll discuss the pathwise optimization (PO) method for stochastic control problem. We will first see how the method produces upper and lower bounds on the optimal value of a high-dimensional optimal stopping problem. The PO methods builds on a dual characterization of optimal stopping problems as optimization problems over the space of martingales. In the second part of the talk, I'll discuss how we can extend the PO method to solve general stochastic control problem.
Reference: Pathwise optimization for optimal stopping problems by V. Desai, V. Farias, C. Moallemi