Title: On nonparametric approaches to stochastic control

Abstract: 

Theoretical solutions to stochastic optimal control problems are well understood in many scenarios; however, their practicability suffers from the assumption of known dynamics of the underlying stochastic process. This raises the challenge of developing purely data-driven strategies, which we explore for ergodic singular control problems associated to continuous diffusions and Lévy processes. In particular, we describe the specific statistical challenges arising in the stochastic control context, and we provide a brief overview of the current state-of-the-art for nonparametric inference of scalar and multidimensional diffusion processes. Finally, we show how these findings translate into exact rates of convergence of polynomial order for the regret for the considered control problems.