Classification of the privacy preserved medical data is the domain of the researchers as it stirs the importance behind hiding the sensitive data from the third-party authenticator. Ensuring the privacy of the medical records and using the disease prediction mechanisms played a remarkable role in peoples' lives such that the earlier detection of the diseases is required for earlier diagnosis. Accordingly, this article proposes a method, named Taylor gradient descent (TGD)-based actor critic neural network (ACNN), which concentrates on performing the medical data classification. Initially, the privacy of the medical data is ensured by using the key matrix developed based on the privacy utility coefficient matrix using the chronological-Whale optimization algorithm. The privacy protected data are subjected to classification by using ACNN that performs the optimal classification using the proposed TGD algorithm. The proposed TGD algorithm is the integration of Taylor series in the gradient descent algorithm that updates the optimal weight of ACNN based on the weights in the previous iterations. The analysis using the Cleveland, Switzerland, and Hungarian dataset proves that the proposed classification strategy obtains an accuracy of 0.9252, a sensitivity of 0.8419, and a specificity of 0.8387, respectively.