Extended Learning Optimality Theory for the XCS classifier system on Multiple Reward Scheme
Motoki Horiuchi, Masaya Nakata · 2021 IEEE Symposium Series on Computational Intelligence (SSCI) · 2021
A restriction of the latest learning optimality theory for the XCS classifier system is that it targets a binary reward scheme, which virtually covers classification domains only. This paper presents an extended learning optimality theory on a multiple reward scheme, where XCS receives a reward sampled from a finite set of multiple rewards. Thus, the multiple reward scheme can be observed in various machine learning problem domains, e.g., prediction, regression, and classification. Our theory firstly proves that XCS can distinguish maximally accurate rules from any other ones with the minimum update times on the multiple-reward scheme. This proof returns theoretically optimal settings of XCS parameters, i.e., a learning rate, an error tolerance, and a subsumption threshold. In addition, suppose a continuous reward scheme as having an extremely large set of discrete rewards, our theory can be substantially satisfied on this scheme.