Even though theoretical solutions to stochastic optimal control problems are well understood in many scenarios, their practicability suffers from the assumption of known dynamics of the underlying stochastic process. This raises the statistical challenge of developing purely data-driven strategies. In this talk we focus on singular control problems associated to diffusions (both one- and multidimensional) and Lévy processes and demonstrate how such data-driven strategies with explicit sublinear regret bounds can be constructed by employing nonparametric statistical techniques.

The talk is based on joint work with Sören Christensen, Asbjørn Holk Thomsen and Claudia Strauch.

Underlying papers:

1) S. Christensen, C. Strauch and L. Trottner. Learning to reflect: A unifying approach for data-driven stochastic control strategies. In: Bernoulli (to appear)

2) S. Christensen, A, Holk Thomsen and L. Trottner. Data-driven rules for multidimensional reflection problems. 2023.

Personal website of Lukas Trottner