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

Abstract

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 fail to achieve accurate solutions within a reasonable number of iterations. To achieve solutions of higher accuracy and high speed, in this paper we propose two proximal quasi-Newtonian limited-memory algorithms -MINFBE applied to the dual problem and the Newtontype alternating minimization algorithm (NAMA) -which can be massively parallelized on lockstep hardware such as graphics processing units (GPUs). We demonstrate the performance of these methods, in terms of convergence speed and parallelizability, on large-scale problems involving millions of variables.

Safe, learning-based MPC for highway driving under lane-change uncertainty: A distributionally robust approach

“…For instance, the increasingly widespread availability of GPUs, even in embedded applications, makes an appealing case for a massively parallelized approach towards solving optimal control problems over the individual scenarios within a tree. (See, e.g, [72,73]. )…”