Reinforced optimal control
This work provides an incremental improvement in the accuracy and efficiency of numerical methods for solving stochastic control problems, which is relevant for researchers and practitioners in quantitative finance and operations research.
This paper extends a reinforced regression method, previously applied to optimal stopping problems, to a broader class of stochastic control problems. The authors demonstrate a considerable improvement in the method's efficiency through numerical examples and theoretical analysis.
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](arXiv:1808.02341) 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.