WIAS Preprint No. 2792, (2020)

Reinforced optimal control



Authors

  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Belomestny, Denis
  • Hager, Paul
  • Pigato, Paolo
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 91G20 93E24

Keywords

  • Reinforced regression, least squares Monte Carlo, stochastic optimal control

DOI

10.20347/WIAS.PREPRINT.2792

Abstract

Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by linear least squares regression. Hence, the choice of basis functions is crucial for the accuracy of the method. Earlier work by some of us [Belomestny, Schoenmakers, Spokoiny, Zharkynbay, Commun. Math. Sci., 18(1):109?121, 2020] proposes to reinforce the basis functions in the case of optimal stopping problems by already computed value functions for later times, thereby considerably improving the accuracy with limited additional computational cost. We extend the reinforced regression method to a general class of stochastic control problems, while considerably improving the method?s efficiency, as demonstrated by substantial numerical examples as well as theoretical analysis.

Download Documents