Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-0882, Japan

CCSE, Japan Atomic Energy Agency, Kashiwa, Chiba 277-0871, Japan

Mathematical Science Team, RIKEN Center for Advanced Intelligence Project (AIP), Chuo, Tokyo 103-0027, Japan

We study the site-diluted double-exchange (DE) model and its effective Ruderman–Kittel–Kasuya–Yosida-like interactions, where localized spins are randomly distributed, with the use of the Self-learning Monte Carlo (SLMC) method. The SLMC method is an accelerating technique for Markov chain Monte Carlo simulation using trainable effective models. We apply the SLMC method to the site-diluted DE model to explore the utility of the SLMC method for random systems. We check the acceptance rates and investigate the properties of the effective models in the strong coupling regime. The effective two-body spin–spin interaction in the site-diluted DE model can describe the original DE model with a high acceptance rate, which depends on temperature and spin concentration. These results support a possibility that the SLMC method could obtain independent configurations in systems with a critical slowing down near a critical temperature or in random systems where a freezing problem occurs in lower temperatures.