## 1 Introduction
Given the possibility of several local optima, most optimization techniques for global issues in deep learning models include a mechanism for balancing the exploration of new regions in the input space against the exploitation of previously high-quality solutions. Automatic search strategies, such as Grid Search (GS) [3] or Cartesian product based hyperparameter search has been developed to solve the limitations of a manual search. Grid Search works on the premise of thorough searching. Grid Search educates a deep learning model on the training sample with all possible hyperparameters and its list of values and assesses its achievement on a cross-validation set using a preset measure. Finally, grid search generates hyperparameters with the best results. Although this method obtains automatic tuning and can potentially obtain the global optimal value of the optimization accusative function, it undergoes the dimensionality curse, which means that the algorithm's efficiency declines as a large number of hyperparameters and its list of values being optimized and the scope of hyperparameter values increases. The Random Search method [3] was suggested to overcome the problem of high computational cost in a grid search, and it was discovered that only a few of the hyperparameters are truly relevant for most data sets. Limiting the examination to non-essential hyperparameters, the overall efficiency may be increased, and the model equation of the optimization function can be achieved. Random search tries a variety of value possibilities at random. It is more efficient in a high-dimensional space than Grid Search [4]. Random search, on the other hand, is unsatisfactory for training some complicated CNN models, as reveals [3]. As a result, getting the automated optimization technique to attain high precision and accuracy has always been an issue in deep learning that has not been entirely solved. A hyperparameter tweaking problem is one in which the optimization goal function is unknown or a black-box function. Conventional optimization approaches such as the Newton's method and gradient descent are ineffective. In this type of optimization issue, Bayesian optimization is a very successful optimization approach [5]. Using the Bayesian formula, it incorporates prior knowledge about the unknown function of the population parameters to produce posterior knowledge about the function probability. Then, using this posterior data, we can figure out where the function gets its best value. The Bayesian optimization technique beats other global optimization methods in experiments [6]. As a result, we proposed the Adaptive Hyperparameter Tuning method based on Bayesian optimization and on the Gaussian process to adjust deep learning hyperparameters. If we assume that the optimization function follows a Gaussian distribution, we may calculate the prior distribution of hyperparameters. The Bayesian optimization approach is based on the Gaussian process will be presented in depth in the following sections. The proposed mechanism is then tested on the proposed CNN Deep-Hist [7] and on three different pretrained deep learning models such as ResNet, DenseNet, and MobileNetV2 to see if it works. Fourfold contributions are evaluated in this work. First, the main theme of this study is to propose Adaptive Hyperparameter Tuning (AHT) for the selection of optimized hyperparameters to classify and analyze medical images. Second, we present a unique stable CNN model for healthcare image classification that incorporates the benefits of the Separable Convolution with a residual learning framework (ResNet) to enhance the exchange of knowledge and development ease. Third, we provide CNN model settings--providing a combination of hyperparameters with fewer parameters, cheaper space and quicker classification, making them more acceptable for healthcare applications. Fourth, we show that optimization algorithms can be effectively used to create CNN categorization designs.