Abstract
In the framework of Markov Decision Processes, we consider the problem of learning a linear approximation of the value function of some fixed policy from one trajectory possibly generated by some other policy. We describe a systematic approach for adapting on-policy learning least squares algorithms of the literature (LSTD [5], LSPE [15], FPKF [7] and GPTD [8]/KTD [10]) to off-policy learning with eligibility traces. This leads to two known algorithms, LSTD(λ)/LSPE(λ) [21] and suggests new extensions of FPKF and GPTD/KTD. We describe their recursive implementation, discuss their convergence properties, and illustrate their behavior experimentally. Overall, our study suggests that the state-of-art LSTD(λ) [21] remains the best least-squares algorithm.
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References
Antos, A., Szepesvári, C., Munos, R.: Learning Near-Optimal Policies with Bellman-Residual Minimization Based Fitted Policy Iteration and a Single Sample Path. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS (LNAI), vol. 4005, pp. 574–588. Springer, Heidelberg (2006)
Baird, L.C.: Residual Algorithms: Reinforcement Learning with Function Approximation. In: ICML (1995)
Bertsekas, D.P., Yu, H.: Projected Equation Methods for Approximate Solution of Large Linear Systems. J. Comp. and Applied Mathematics 227(1), 27–50 (2009)
Bertsekas, D.P., Tsitsiklis, J.N.: Neuro-Dynamic Programming. Athena Scientific (1996)
Boyan, J.A.: Technical Update: Least-Squares Temporal Difference Learning. Machine Learning 49(2-3), 233–246 (1999)
Bradtke, S.J., Barto, A.G.: Linear Least-Squares algorithms for temporal difference learning. Machine Learning 22(1-3), 33–57 (1996)
Choi, D., Van Roy, B.: A Generalized Kalman Filter for Fixed Point Approximation and Efficient Temporal-Difference Learning. DEDS 16, 207–239 (2006)
Engel, Y.: Algorithms and Representations for Reinforcement Learning. Ph.D. thesis, Hebrew University (2005)
Geist, M., Pietquin, O.: Eligibility Traces through Colored Noises. In: ICUMT (2010)
Geist, M., Pietquin, O.: Kalman Temporal Differences. JAIR 39, 483–532 (2010)
Geist, M., Pietquin, O.: Parametric Value Function Approximation: a Unified View. In: ADPRL (2011)
Kearns, M., Singh, S.: Bias-Variance Error Bounds for Temporal Difference Updates. In: COLT (2000)
Maei, H.R., Sutton, R.S.: GQ(λ): A general gradient algorithm for temporal-difference prediction learning with eligibility traces. In: Conference on Artificial General Intelligence (2010)
Munos, R.: Error Bounds for Approximate Policy Iteration. In: ICML (2003)
Nedić, A., Bertsekas, D.P.: Least Squares Policy Evaluation Algorithms with Linear Function Approximation. DEDS 13, 79–110 (2003)
Precup, D., Sutton, R.S., Singh, S.P.: Eligibility Traces for Off-Policy Policy Evaluation. In: ICML (2000)
Ripley, B.D.: Stochastic Simulation. Wiley & Sons (1987)
Scherrer, B.: Should one compute the Temporal Difference fix point or minimize the Bellman Residual? The unified oblique projection view. In: ICML (2010)
Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction (Adaptive Computation and Machine Learning), 3rd edn. MIT Press (1998)
Tsitsiklis, J., Van Roy, B.: An analysis of temporal-difference learning with function approximation. IEEE Transactions on Automatic Control 42(5), 674–690 (1997)
Yu, H.: Convergence of Least-Squares Temporal Difference Methods under General Conditions. In: ICML (2010)
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Scherrer, B., Geist, M. (2012). Recursive Least-Squares Learning with Eligibility Traces. In: Sanner, S., Hutter, M. (eds) Recent Advances in Reinforcement Learning. EWRL 2011. Lecture Notes in Computer Science(), vol 7188. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29946-9_14
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DOI: https://doi.org/10.1007/978-3-642-29946-9_14
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