Least Squares Policy Iteration with Instrumental Variables vs. Direct Policy Search: Comparison Against Optimal Benchmarks Using Energy Storage

Abstract: This paper studies approximate policy iteration (API) methods which use least-squares Bellman error minimization for policy evaluation. We address several of its enhancements, namely, Bellman error minimization using instrumental variables, least-squares projected Bellman error minimization, and projected Bellman error minimization using instrumental variables. We prove that for a general discrete-time stochastic control problem, Bellman error minimization using instrumental variables is equivalent to both variants of projected Bellman error minimization. An alternative to these API methods is direct policy search based on knowledge gradient. The practical performance of these three approximate dynamic programming methods are then investigated in the context of an application in energy storage, integrated with an intermittent wind energy supply to fully serve a stochastic time-varying electricity demand. We create a library of test problems using real-world data and apply value iteration to find their optimal policies. These benchmarks are then used to compare the developed policies. Our analysis indicates that API with instrumental variables Bellman error minimization prominently outperforms API with least-squares Bellman error minimization. However, these approaches underperform our direct policy search implementation.