We design a new adaptive learning algorithm for misclassification cost problems that attempt to reduce the cost of misclassified instances derived from the consequences of various errors. Our algorithm (adaptive cost sensitive learning - AdaCSL) adaptively adjusts the loss function such that the classifier bridges the difference between the class distributions between subgroups of samples in the training and test data sets with similar predicted probabilities (i.e., local training-test class distribution mismatch). We provide some theoretical performance guarantees on the proposed algorithm and present empirical evidence that a deep neural network used with the proposed AdaCSL algorithm yields better cost results on several binary classification data sets that have class-imbalanced and class-balanced distributions compared to other alternative approaches.