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This paper studies approximate policy iteration (API) methods which useleast-squares Bellman error minimization for policy evaluation. We addressseveral of its enhancements, namely, Bellman error minimization usinginstrumental variables, least-squares projected Bellman error minimization, andprojected Bellman error minimization using instrumental variables. We provethat for a general discrete-time stochastic control problem, Bellman errorminimization using instrumental variables is equivalent to both variants ofprojected Bellman error minimization. An alternative to these API methods isdirect policy search based on knowledge gradient. The practical performance ofthese three approximate dynamic programming methods are then investigated inthe context of an application in energy storage, integrated with anintermittent wind energy supply to fully serve a stochastic time-varyingelectricity demand. We create a library of test problems using real-world dataand apply value iteration to find their optimal policies. These benchmarks arethen used to compare the developed policies. Our analysis indicates that APIwith instrumental variables Bellman error minimization prominently outperformsAPI with least-squares Bellman error minimization. However, these approachesunderperform our direct policy search implementation.

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