Randomized Operating Point Selection in Adversarial Classification

Abstract

Security systems for email spam filtering, network intrusion detection, steganalysis, and watermarking, frequently use classifiers to separate malicious behavior from legitimate. Typically, they use a fixed operating point minimizing the expected cost / error. This allows a rational attacker to deliver invisible attacks just below the detection threshold. We model this situation as a non-zero sum normal form game capturing attacker’s expected payoffs for detected and undetected attacks, and detector’s costs for false positives and false negatives computed based on the Receiver Operating Characteristic (ROC) curve of the classifier. The analysis of Nash and Stackelberg equilibria reveals that using a randomized strategy over multiple operating points forces the rational attacker to design less efficient attacks and substantially lowers the expected cost of the detector. We present the equilibrium strategies for sample ROC curves from network intrusion detection system and evaluate the corresponding benefits.