iLSTD: Eligibility Traces and Convergence Analysis

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Alborz Geramifard, Michael Bowling, Martin Zinkevich, Richard S. Sutton


We present new theoretical and empirical results with the iLSTD algorithm for policy evaluation in reinforcement learning with linear function approximation. iLSTD is an incremental method for achieving results similar to LSTD, the dataefficient, least-squares version of temporal difference learning, without incurring the full cost of the LSTD computation. LSTD is O(n2 ), where n is the number of parameters in the linear function approximator, while iLSTD is O(n). In this paper, we generalize the previous iLSTD algorithm and present three new results: (1) the first convergence proof for an iLSTD algorithm; (2) an extension to incorporate eligibility traces without changing the asymptotic computational complexity; and (3) the first empirical results with an iLSTD algorithm for a problem (mountain car) with feature vectors large enough (n = 10, 000) to show substantial computational advantages over LSTD.