A utilitarian approach to adversarial learning in credit card fraud detection

Credit card fraud detection can be modeled as an adversarial game between a fraudster and the fraud detection mechanism. Previous work uses a game theoretical adversarial learning approach to model the most successful strategy and preemptively adapt the fraud detection system. The game consists of the adversary's selection of strategy and the fraud detection system's decision to retrain. In the previous work, the detection system is retrained every round of the game. In application, there may be costs and risks associated with training and deploying a new model. Thus, it may be desirable to optimize the decision of whether to retrain the model based on the expected economic disutility. The presented work addresses this desire by using a utilitarian approach to optimally decide whether to retrain the classifier by comparing the economic values of the new and old classifiers. A framework from decision theory is derived within the context of credit card fraud. Further, we show how a utility function can be used to identify the best fraud strategy in economic terms. We add to the literature by extending the adversarial learning model developed in previous work to include a theoretical framework for retraining when it is economically advantageous and judging fraud strategies on their economic cost. Our approaches are tested against the decisions to always retrain and to never retrain.