Wednesday, April 10, 2019 - 15:00 in V3-201
Nonparametric learning in stochastic control - exploration vs. exploitation
A talk in the Bielefeld Stochastic Afternoon series by
Sören Christensen from University of Hamburg
| Abstract: |
One of the fundamental assumptions in stochastic control of continuous time processes is that the dynamics of the underlying (diffusion) process is known. This is, however, usually obviously not fulfilled in practice. On the other hand, over the last decades, a rich theory for nonparametric estimation of the drift (and volatility) for continuous time processes has been developed. The aim of this talk is to make a first (small) step to bringing together techniques from stochastic control with methods from statistics for stochastic processes to find a way to both learn the dynamics of the underlying process and control good at the same time. To this end, we study a toy example motivated from optimal harvesting, mathematically described as an impulse control problem. One of the problems that immediately arises is an Exploration vs. Exploitation behavior as is well known in Machine Learning. We propose a way to deal with this issue and analyse the proposed strategy asymptotically.
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