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

TL;DR

This paper introduces two parallelizable proximal quasi-Newton algorithms, MinFBE and NAMA, designed for large-scale stochastic optimal control problems, demonstrating improved convergence and scalability on GPU hardware.

Contribution

The paper presents novel proximal quasi-Newton methods that are highly parallelizable and effective for solving large-scale stochastic optimal control problems.

Findings

Algorithms achieve faster convergence on large problems.

Methods scale efficiently on GPU hardware.

Demonstrated effectiveness on problems with millions of variables.

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 Newton-type 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.