The optimization method is one of key issues in discriminative learning of pattern classifiers. This paper proposes a hybrid approach of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and the gradient decent method for optimizing Bayesian classifiers under the SOFT target based Max-Min posterior Pseudo-probabilities (Soft-MMP) learning framework. In our hybrid optimization approach, the weighted mean of the parent population in the CMA-ES is adjusted by exploiting the gradient

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... rmation of objective function, based on which the offspring is generated. As a result, the efficiency and the effectiveness of the CMA-ES are improved. We apply the Soft-MMP with the proposed hybrid optimization approach to handwritten digit recognition. The experiments on the CENPARMI database show that our handwritten digit classifier outperforms other state-of-the-art techniques. Furthermore, our hybrid optimization approach behaved better than not only the single gradient decent method but also the single CMA-ES in the experiments.