Least Squares Monte Carlo Approach to Convex Control Problems

Optimal control problems with convex functions are ubiquitous in applications of stochastic optimization. However, when applied in this context, the classical least squares Monte Carlo methodology makes no attempt to take advantage of this special structure: Given the convexity of value functions, it seems reasonable to search for the best least-squares fit among the elements of a cone of convex functions, rather than among a linear space of feature functions as required by the classical least squares Monte Carlo approach. In the present work, we build on this idea by introducing an appropriate modification to the classical method. We show that computation time and accuracy can be improved by using projections on convex cones instead of projections onto linear spaces.