Simulation Methods for Stochastic Storage Problems: A Statistical Learning Perspective

TL;DR

This paper introduces the dynamic emulation algorithm (DEA), a unified framework for solving stochastic storage problems using regression Monte Carlo methods from a statistical learning perspective, emphasizing regression architecture and experimental design.

Contribution

It develops the DEA framework that unifies existing approaches, incorporating Gaussian process regression and adaptive experimental designs for improved stochastic storage problem solutions.

Findings

Gaussian process regression enhances modeling flexibility.

Adaptive experimental designs outperform traditional grid methods.

DEA provides a modular, versatile approach for stochastic storage applications.

Abstract

We consider solution of stochastic storage problems through regression Monte Carlo (RMC) methods. Taking a statistical learning perspective, we develop the dynamic emulation algorithm (DEA) that unifies the different existing approaches in a single modular template. We then investigate the two central aspects of regression architecture and experimental design that constitute DEA. For the regression piece, we discuss various non-parametric approaches, in particular introducing the use of Gaussian process regression in the context of stochastic storage. For simulation design, we compare the performance of traditional design (grid discretization), against space-filling, and several adaptive alternatives. The overall DEA template is illustrated with multiple examples drawing from natural gas storage valuation and optimal control of back-up generator in a microgrid.