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Rule reduction by selection strategy in XCS with adaptive action map

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Abstract

The XCS classifier system is a rule-based evolutionary machine learning system. XCS evolves classifiers in order to learn generalized solutions. The XCS with adaptive action mapping (XCSAM) is inherited from XCS, which evolves a best action map where it evolves classifiers that advocate the best action in every state. Accordingly, XCSAM can potentially evolve solutions that are more compact than XCS, which in contrast focuses on a complete action map. Previous experimental results however have shown that, in some problems, XCSAM may produce solutions with more classifiers than XCS. In this paper, we initially show that the original fitness-based selection strategy of XCS produces non effective classifiers which are not likely to be in the best action map (i.e., they are inaccurate ones or do not have best actions) in XCSAM. Then, we introduce a new selection strategy for XCSAM that promotes the evolution of classifiers advocating the best action map and thus produces more compact solutions. The new strategy selects classifiers based both on their fitness (like XCS) and on the parameter optimality of action of XCSAM. The result is a pressure towards classifiers that are accurate and advocate the best actions. We present analyses showing that the new selection strategy successfully enables XCSAM to focus on classifiers having best actions. Our experimental results show that XCSAM with the new selection strategy (called XCSAM-SS) can evolve smaller solutions than XCS (and the original XCSAM) both in single-step and multi-step problems. As a consequence, XCSAM can also learn with smaller iterations than XCS in the single-step problem. Our conclusion is that, as the best action map potentially has a compact solution, XCSAM evolves a much compact solution than XCS by adding an adequate selection strategy.

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Notes

  1. XCSAM uses the selection array for single-step problems because in these problems it sometimes overestimates the system prediction for the not-best actions. This happens because it is easy for XCSAM to find a pure best action map when there are only two possible rewards. But sometimes mutation changes the action of a classifier from best to not-best action and the offspring temporarily inherits the high prediction of the parent. This has been observed in single-step problems but not in multi-step problems. We hypothesis this problem does not occur in multi-step problems because XCSAM does not find a pure best action map [25] but finds an adaptive action map where some not-best actions remain to keep generalized classifiers; and the not-best actions in it prevent occasional mutations from changing the max system prediction.

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Acknowledgments

This work was supported by the JSPS Institutional Program.

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Authors and Affiliations

  1. Graduate School of Informatics, The University of Electro-Communications, Chofu, 182-0021, Japan

    Masaya Nakata & Keiki Takadama

  2. Japan Society for the Promotion of Science, Chiyoda-ku, 102-0083, Japan

    Masaya Nakata

  3. Department of Electronics and Information, Politecnico di Milano, 20133, Milan, Italy

    Pier Luca Lanzi

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  1. Masaya Nakata
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  2. Pier Luca Lanzi
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Correspondence to Masaya Nakata.

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Nakata, M., Lanzi, P.L. & Takadama, K. Rule reduction by selection strategy in XCS with adaptive action map. Evol. Intel. 8, 71–87 (2015). https://doi.org/10.1007/s12065-015-0130-1

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