Bayesian Algorithms Learn to Stabilize Unknown Stochastic Differential Equations

• Activity Number: 34 - Advanced Methods in Statistical Learning
• Type: Contributed
• Date/Time: Sunday, August 7, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Mohamad Kazem Shirani Faradonbeh*
• Companies: University of Georgia
• Keywords: Posterior sampling; Unknown SDE; Unstable data; Bayesian learning; Stabilization under uncertainty; Reinforcement learning

Abstract

Multidimensional linear stochastic differential equations are canonical models for dynamic environments. In many applications, the true drift matrices are unknown and need to be learned from the trajectory data. An important problem is to ensure that the environment can be stabilized by appropriately designed exogenous inputs, despite uncertainties about the drift matrices. So, a reliable data-driven stabilization procedure needs to learn fast from unstable data. We provide theoretical learning accuracies for that purpose and propose a novel Bayesian algorithm that learns to stabilize unknown stochastic differential equations. The presented algorithm utilizes posterior sampling, is computationally fast and flexible, and exposes effective learning performance after a very short time period of interacting with the environment.