Sample from the Posterior to Stabilize an Unknown Diffusion Process

Music City Center 

Multidimensional diffusion processes are classical models for dynamics of highly stochastic phenomena. The range of applications spans from early-stage cancer treatments to monetary policies for controlling inflation. Accordingly, the exogenous control input of the diffusion process needs to be delicately designed to stabilize the dynamics and preclude wild growths. In many situations that involve uncertainties, one needs to apply input signals and estimate the unknown parameters in order to learn stabilizing control policies. We propose a data-driven algorithm for this task that employs random inputs and forms a posterior belief about the model parameters. Then, we show that by treating posterior samples as true parameters, the process can be stabilized with high probability.

Diffusion Processes

Random Input

Stabilization

Posterior Sampling 

Section on Statistics and the Environment