SPOCK: A proximal method for multistage risk-averse optimal control problems

TL;DR

This paper introduces SPOCK, a GPU-accelerated proximal algorithm for large-scale, multistage risk-averse optimal control problems, combining splitting techniques with acceleration methods for improved efficiency.

Contribution

The paper presents a novel splitting method for risk-averse control problems and a new solver, SPOCK, that leverages GPU computing and advanced acceleration schemes.

Findings

Efficient computation of risk-averse control problems on GPU hardware.

SPOCK demonstrates faster convergence using SuperMann and Anderson's acceleration.

Open-source Julia implementation allows for warm-starting and parallelization.

Abstract

Risk-averse optimal control problems have gained a lot of attention in the last decade, mostly due to their attractive mathematical properties and practical importance. They can be seen as an interpolation between stochastic and robust optimal control approaches, allowing the designer to trade-off performance for robustness and vice-versa. Due to their stochastic nature, risk-averse problems are of a very large scale, involving millions of decision variables, which poses a challenge in terms of efficient computation. In this work, we propose a splitting for general risk-averse problems and show how to efficiently compute iterates on a GPU-enabled hardware. Moreover, we propose Spock - a new algorithm that utilizes the proposed splitting and takes advantage of the SuperMann scheme combined with fast directions from Anderson's acceleration method for enhanced convergence speed. We implement Spock in Julia as an open-source solver, which is amenable to warm-starting and massive parallelization.