Abstract
Reinforcement learning is one of the most reliable methods, which have been used to solve many problems. One of the best reinforcement learning family methods are temporal difference methods. The most important weakness of reinforcement learning methods, such as temporal difference methods, is that these methods have slow convergence rate. Many studies are devoted to solving this problem. One of the proposed solutions to this problem is eligibility traces. Owing to the nature of off-policy methods, combining eligibility traces with off-policy methods requires special attention. In the early learning process for Watkins method (one of the dominant eligibility traces methods), cutting eligibility traces during exploratory actions results in diminishing benefits of eligibility traces method. In this study, we propose a framework to combine eligibility traces with off-policy methods. This research attempts to properly use the information explored during action exploration of the agent; to this end, the decision about applying the eligibility traces during the exploratory actions of the agent is made by means of fuzzy adaptation. We apply this method to find the goal state in the static and dynamic grid world. We compare our approach against the state of the art techniques and show that it outperforms these techniques both in terms of averaged achieved reward and also the convergence time.
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Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (2018)
Van Seijen, H., Mahmood, A.R., Pilarski, P.M., Machado, M.C., Sutton, R.S.: True online temporal-difference learning. J. Mach. Learn. Res. 17(1), 5057–5096 (2016)
Boyan, J.A.: Technical update: least-squares temporal difference learning. Mach. Learn. 49(2–3), 233–246 (2002)
Choi, D., Van Roy, B.: A generalized kalman filter for fixed point approximation and efficient temporal-difference learning. Discrete Event Dyn. Syst. 16(2), 207–239 (2006)
Yu, H., Bertsekas, D.P.: Convergence results for some temporal difference methods based on least squares. IEEE Trans. Autom. Control 54(7), 1515–1531 (2009)
Maei, H.R., Szepesvári, C., Bhatnagar, S., Sutton, R.S.: Toward off-policy learning control with function approximation. In: ICML, pp. 719–726 (2010)
Sutton, R.S., Maei, H.R., Precup, D., Bhatnagar, S., Silver, D., Szepesvári, C., Wiewiora, E.: Fast gradient-descent methods for temporal-difference learning with linear function approximation, In: Proceedings of the 26th Annual International Conference on Machine Learning, 993–1000. ACM (2009)
Maei, H.R., Sutton, R.S.: Gq (\(\lambda\)): a general gradient algorithm for temporal-difference prediction learning with eligibility traces. In: Proceedings of the Third Conference on Artificial General Intelligence, vol. 1, pp. 91–96 (2010)
Geist, M., Scherrer, B.: Off-policy learning with eligibility traces: a survey. J. Mach. Learn. Res. 15(1), 289–333 (2014)
Gehring, C., Pan, Y., White, M.: Incremental truncated lstd, arXiv preprint arXiv:1511.08495 (2015)
Pan, Y., White, A.M., White, M.: Accelerated gradient temporal difference learning. In: AAAI, 2464–2470 (2017)
Devraj, A.M., Meyn, S.P.: Fastest convergence for q-learning, arXiv preprint arXiv:1707.03770 (2017)
Chen, S.-L., Wei, Y.-M.: Least-squares sarsa (lambda) algorithms for reinforcement learning, In: Natural Computation, 2008. ICNC’08. Fourth International Conference on, vol. 2, pp. 632–636, IEEE (2008)
Kaelbling, L.P., Littman, M.L., Moore, A.W.: Reinforcement learning: a survey. J. Artif. Intell. Res. 4, 237–285 (1996)
Engel, Y.: Algorithms and Representations for Reinforcement Learning. Hebrew University of Jerusalem, Jerusalem (2005)
Dolk, V.: Survey Reinforcement Learning. Eindhoven University of Technology, Eindhoven (2010)
Glorennec, P.Y., Jouffe, L.: Fuzzy q-learning. In: Proceedings of 6th International Fuzzy Systems Conference, vol. 2, 659–662 (1997)
Er, M.J., Deng, C.: Online tuning of fuzzy inference systems using dynamic fuzzy q-learning. IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) 34(3), 1478–1489 (2004)
Buşoniu, L., Ernst, D., De Schutter, B., Babuška, R.: Continuous-state reinforcement learning with fuzzy approximation, In: Adaptive Agents and Multi-Agent Systems III. Adaptation and Multi-Agent Learning, pp. 27–43, Springer, London (2008)
Bonarini, A., Lazaric, A., Montrone, F., Restelli, M.: Reinforcement distribution in fuzzy q-learning. Fuzzy Sets Syst. 160(10), 1420–1443 (2009)
Zajdel, R.: Fuzzy q(\(\lambda\))-learning algorithm. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. (Berlin, Heidelberg), pp. 256–263, Springer, Berlin (2010)
Watkins, C.J.C.H.: Learning from delayed rewards. Ph.D thesis, King’s College, Cambridge (1989)
Peng, J., Williams, R.J.: Incremental multi-step q-learning, In: Machine Learning Proceedings 1994, 226–232. Elsevier, Amsterdam (1994)
Sutton, R., Barto, A.: Reinforcement Learning. MIT Press, Cambridge (1998)
Leng, J., Fyfe, C., Jain, L.C.: Experimental analysis on sarsa (\(\lambda\)) and q (\(\lambda\)) with different eligibility traces strategies. J. Intell. Fuzzy Syst. 20(1,2), 73–82 (2009)
Even-Dar, E., Mansour, Y.: Learning rates for q-learning. J. Mach. Learn. Res. 5, 1–25 (2003). no. Dec
Tizhoosh, H.: Opposition-based reinforcement learning. JACIII 10(01), 578–585 (2006)
Azar, M.G., Munos, R., Ghavamzadeh, M., Kappen, H.: Speedy q-learning, In: Advances in Neural Information Processing Systems (2011)
Devraj, A.M., Meyn, S.: Zap q-learning, In: Advances in Neural Information Processing Systems, 2235–2244 (2017)
Wang, L.: A Couse in Fuzzy Systems and Control. Prentice-Hall, London (1997)
Dai, X., Li, C.-K., Rad, A.B.: An approach to tune fuzzy controllers based on reinforcement learning for autonomous vehicle control. IEEE Trans. Intell. Transp. Syst. 6(3), 285–293 (2005)
Schneider, T.D.: Information theory primer with an appendix on logarithms. In: National Cancer Institute, Citeseer (2007)
Borda, M.: Fundamentals in Information Theory and Coding. Springer, Berlin (2011)
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Shokri, M., Khasteh, S.H. & Aminifar, A. Adaptive Fuzzy Watkins: A New Adaptive Approach for Eligibility Traces in Reinforcement Learning. Int. J. Fuzzy Syst. 21, 1443–1454 (2019). https://doi.org/10.1007/s40815-019-00633-x
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DOI: https://doi.org/10.1007/s40815-019-00633-x