Approximate Dynamic Programming Using Model-Free Bellman Residual Elimination

This paper presents an modification to the method of Bellman Residual Elimination (BRE) [1], [2] for approximate dynamic programming. While prior work on BRE has focused on learning an approximate policy for an underlying Markov Decision Process (MDP) when the state transition model of the MDP is known, this work proposes a model-free variant of BRE that does not require knowledge of the state transition model. Instead, state trajectories of the system, generated using simulation and/or observations of the real system in operation, are used to build stochastic approximations of the quantities needed to carry out the BRE algorithm. The resulting algorithm can be shown to converge to the policy produced by the nominal, model-based BRE algorithm in the limit of observing an infinite number of trajectories. To validate the performance of the approach, we compare model-based and model-free BRE against LSPI [3], a well-known approximate dynamic programming algorithm. Measuring performance in terms of both computational complexity and policy quality, we present results showing that BRE performs at least as well as, and sometimes significantly better than, LSPI on a standard benchmark problem.