The temporal-difference methods TD( @math ) and Sarsa( @math ) form a core part of modern reinforcement learning. Their appeal comes from their good performance, low computational cost, and their simple interpretation, given by their forward view. Recently, new versions of these methods were introduced, called true online TD( @math ) and true online Sarsa( @math ), respectively (van Seijen & Sutton, 2014). These new versions maintain an exact equivalence with the forward view at all times, whereas the traditional versions only approximate it for small step-sizes. We hypothesize that these true online methods not only have better theoretical properties, but also dominate the regular methods empirically. In this article, we put this hypothesis to the test by performing an extensive empirical comparison. Specifically, we compare the performance of true online TD( @math ) Sarsa( @math ) with regular TD( @math ) Sarsa( @math ) on random MRPs, a real-world myoelectric prosthetic arm, and a domain from the Arcade Learning Environment. We use linear function approximation with tabular, binary, and non-binary features. Our results suggest that the true online methods indeed dominate the regular methods. Across all domains representations the learning speed of the true online methods are often better, but never worse than that of the regular methods. An additional advantage is that no choice between traces has to be made for the true online methods. Besides the empirical results, we provide an in-depth analysis of the theory behind true online temporal-difference learning. In addition, we show that new true online temporal-difference methods can be derived by making changes to the online forward view and then rewriting the update equations.
Furthermore, @cite_0 derived backward views for a series of increasingly complex forward views. The derivation of the true online TD( @math ) equations in Appendix is similar to those derivations.
@cite_0
1597303641
TD( ) is a popular family of algorithms for approximate policy evaluation in large MDPs. TD( ) works by incrementally updating the value function after each observed transition. It has two major drawbacks: it makes ine cient use of data, and it requires the user to manually tune a stepsize schedule for good performance. For the case of linear value function approximations and = 0, the Least-Squares TD (LSTD) algorithm of Bradtke and Barto (Bradtke and Barto, 1996) eliminates all stepsize parameters and improves data e ciency. This paper extends Bradtke and Barto's work in three signi cant ways. First, it presents a simpler derivation of the LSTD algorithm. Second, it generalizes from = 0 to arbitrary values of ; at the extreme of = 1, the resulting algorithm is shown to be a practical formulation of supervised linear regression. Third, it presents a novel, intuitive interpretation of LSTD as a model-based reinforcement learning technique.