Probabilistic error analysis for some approximation schemes to optimal control problems
Abstract
We introduce a class of numerical schemes for optimal control problems based on a novel Markov chain approximation, which uses, in turn, a piecewise constant policy approximation, Euler-Maruyama time stepping, and a Gauss-Hermite approximation of the Gaussian increments. We provide lower error bounds of order arbitrarily close to 1/2 in time and 1/3 in space for Lipschitz viscosity solutions, coupling probabilistic arguments with regularization techniques as introduced by Krylov. The corresponding order of the upper bounds is 1/4 in time and 1/5 in space. For sufficiently regular solutions, the order is 1 in both time and space for both bounds. Finally, we propose techniques for further improving the accuracy of the individual components of the approximation.
Cite
@article{arxiv.1810.04691,
title = {Probabilistic error analysis for some approximation schemes to optimal control problems},
author = {Athena Picarelli and Christoph Reisinger},
journal= {arXiv preprint arXiv:1810.04691},
year = {2020}
}