XCSR with VAE using Gaussian Distribution Matching: From Point to Area Matching in Latent Space for Less-overlapped Rule Generation in Observation Space

Abstract

This paper focuses on the matching mechanism of Learning Classifier System (LCS) in a continuous space and proposes a novel matching mechanism based on Gaussian distribution. This mechanism can match the “area” instead of the “point (one value)” in the continuous space unlike the conventional LCS such as XCSR (XCS with Continuous-Valued Inputs). Such an area matching contributes to generating the rules (called classifiers) with less-overlapped with other rules. Concretely, the proposed area matching mechanism employed in XCSR using VAE can generate appropriate classifiers for latent variables with high-dimensional inputs by VAE and create a human-interpretable observation space of human-interpretable classifiers. Since the latent variable in VAE is followed by Gaus-sian distribution, the following three matching mechanisms are compared: (i) the (single) point matching that selects the classifier which condition covers the mean of Gaussian distribution M; (ii) the multiple points matching that selects the classifier which condition covers the data sampled from Gaussian distribution (M, u); and (iii) the area matching that selects the classifier which condition roughly covers a certain area of Gaussian distribution (M, o). Through the intensive experiments on the high dimension maze problem, the following implications have been revealed: (1) the point matching in XCSR with VAE generates the ambiguous classifiers which conditions are overlapped with the other classifiers with the different action; (2) the sampling multiple points matching in XCSR with VAE has a potential of generating the less-overlapped classifiers by improving the data set through sampling. (3) the proposed area matching can generate the less-overlapped classifiers with the same learning steps, which corresponds to the time of the point matching.