Iterative minimization algorithms appear in various areas including machine learning, neural network, and information theory. The em algorithm is one of the famous one in the former area, and Arimoto-Blahut algorithm is a typical one in the latter area. However, these two topics had been separately studied for a long time. In this paper, we generalize an algorithm that was recently proposed in the context of Arimoto-Blahut algorithm. Then, we show various convergence theorems, one of which covers the case when each iterative step is done approximately. Also, we apply this algorithm to the target problem in em algorithm, and propose its improvement. In addition, we apply it to other various problems in information theory.

翻译：迭代最小化算法在各个领域中出现，包括机器学习、神经网络和信息理论。EM算法是前者中著名的一种方法，而Arimoto-Blahut算法则是后者中典型的算法。然而，这两个主题长期以来一直被分别研究。在本文中，我们扩展了最近在Arimoto-Blahut算法中提出的算法。然后，我们展示了各种收敛定理，其中一些收敛定理涵盖了每个迭代步骤被近似完成的情况。此外，我们将此算法应用于EM算法中的目标问题，并提出了改进方法。此外，我们将其应用于信息理论中的各种问题。