Least Squares Monte Carlo and Pathwise Optimization for Merchant Energy Production

43 Pages Posted: 9 Aug 2021

See all articles by Bo Yang

Bo Yang

Carnegie Mellon University - Tepper School of Business

Selvaprabu Nadarajah

University of Illinois at Chicago - College of Business Administration

Nicola Secomandi

Carnegie Mellon University - David A. Tepper School of Business

Date Written: July 30, 2021

Abstract

We study merchant energy production modeled as a compound switching and timing option. The resulting Markov decision process is intractable. Least squares Monte Carlo combined with information relaxation and duality is a state-of-the-art reinforcement learning methodology to obtain operating policies and optimality gaps for related models. Pathwise optimization is a competing technique developed for optimal stopping settings, in which it typically provides superior results compared to this approach, albeit with a larger computational effort. We apply these procedures to merchant energy production. Employing pathwise optimization requires methodological extensions. We use principal component analysis and block coordinate descent in novel ways to respectively precondition and solve the ensuing ill-conditioned and large scale linear program, which even a cutting-edge commercial solver is unable to handle directly. Both techniques yield near optimal operating policies on realistic ethanol production instances. However, at the cost of both considerably longer run times and greater memory usage, pathwise optimization leads to substantially tighter dual bounds compared to least squares Monte Carlo, even when specified in a simple fashion, complementing it in this case. Thus, it plays a critical role in obtaining small optimality gaps. Our numerical observations on the magnitudes of these bound improvements differ from what is currently known. This research has potential relevance for other commodity merchant operations contexts and motivates additional algorithmic work in the area of pathwise optimization.

Keywords: Block coordinate descent, information relaxation and duality, least squares Monte Carlo, Markov decision processes, merchant energy operations, pathwise optimization, principal component analysis, real options, reinforcement learning

JEL Classification: C02, C61, D24, G11, L6, L7

Suggested Citation

Yang, Bo and Nadarajah, Selvaprabu and Secomandi, Nicola, Least Squares Monte Carlo and Pathwise Optimization for Merchant Energy Production (July 30, 2021). Available at SSRN: https://ssrn.com/abstract=3900797 or http://dx.doi.org/10.2139/ssrn.3900797

Bo Yang

Carnegie Mellon University - Tepper School of Business ( email )

Pittsburgh, PA 15213-3890
United States

Selvaprabu Nadarajah (Contact Author)

University of Illinois at Chicago - College of Business Administration ( email )

601 South Morgan Street
Chicago, IL 60607
United States

Nicola Secomandi

Carnegie Mellon University - David A. Tepper School of Business ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213-3890
United States

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