A The learning process of machine learning consists of finding values of unknown weights in a cost function by minimizing the cost function based on learning data. However, since the cost function is not convex, it is conundrum to find the minimum value of the cost function. The existing methods used to find the minimum values usually use the first derivative of the cost function. When even the local minimum (but not a global minimum) is reached, since the first derivative of the cost function becomes zero, the methods give the local minimum values, so that the desired global minimum cannot be found. To overcome this problem, in this paper we modified one of the existing schemes—the adaptive momentum estimation scheme—by adding a new term, so that it can prevent the new optimizer from staying at local minimum. The convergence condition for the proposed scheme and the convergence value are also analyzed, and further explained through several numerical experiments whose cost function is non-convex.
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