Mike Ludkovski

Title: Connecting Optimal Switching Control and Sequential Design

 

Abstract: Numerous problems in dynamic optimization of energy assets can be
represented in terms of stochastic optimal switching control. In such
settings, decision-making is reduced to identifying the best current action
among a finite set of choices, for example “pump” vs “withdraw” vs “hold”.
In turn, this necessitates comparing several expected costs-to-go
functionals across a typically multi-dimensional, continuous state space. We
propose to reformulate this context as a statistical problem of identifying
the maximal response among L >=2 unknown response surfaces that can be
noisily sampled through a Monte Carlo simulator. While similar in flavor to
Multi-Armed Bandits and Active Learning frameworks, our setting  requires
joint experimental design both in space and response-index dimensions. To
maximize computational efficiency, we propose several novel acquisition
functions for the respective sequential design of experiments, including the
Gap-UCB and Gap-SUR heuristics. Numerical examples using both synthetic data
and a case study in capacity expansion of power generation based on Aid et
al (2012) are provided to illustrate our approach. (Joint work with R. Hu
(UCSB)).