Massively parallelizable proximal algorithms for large‐scale stochastic optimal control problems

Scenario‐based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First‐order methods are suitable as they can deal with such large‐scale problems, but may perform poorly and fail to converge within a reasonable number of iterations. To achieve a fast rate of convergence and high solution speeds, in this article, we propose the use of two proximal quasi‐Newtonian limited‐memory algorithms—minfbe applied to the dual problem and the Newton‐type alternating minimization algorithm (nama)—which can be massively parallelized on lockstep hardware such as graphics processing units. In particular, we use minfbe and nama to solve scenario‐based stochastic optimal control problems with affine dynamics, convex quadratic cost functions (with the stage cost functions being strongly convex in the control variable) and joint state‐input convex constraints. We demonstrate the performance of these methods, in terms of convergence speed and parallelizability, on large‐scale problems involving millions of variables.