AMS Weekly Seminar | Enlu Zhou

Location: Krieger 205

When: October 23rd at 1:30 p.m.

Title: Bayesian Learning for Data-driven Dynamic Stochastic Optimization

Abstract: In many dynamic stochastic optimization models, including multi-stage stochastic program, stochastic optimal control (SOC), and Markov decision process (MDP), distributions of the randomness are never precisely known in practice and are typically estimated by data. Assuming a parametric form of the randomness distribution, we take a Bayesian approach to learn the unknown distribution parameter from streaming data and propose a Bayesian risk re-formulation of the original problem. The Bayesian posterior distribution can be treated as a state augmented to the original state, leading to a higher-dimensional continuous-state problem. While this approach theoretically provides the optimal control policy, it can be challenging to solve numerically. Therefore, we further propose an episodic approach that only updates the posterior periodically and solves a Bayesian counterpart problem under the fixed posterior in each period. Theoretical convergence results and computational methods will be discussed.

Zoom link: https://wse.zoom.us/j/93600407710?pwd=JBL8VsObRxX6MkhdjAUxCadqJDoZrZ.1