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. © 2023 The Authors. Optimal Control Applications and Methods published by John Wiley & Sons Ltd.