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Many recent works have proposed methods to train classifiers with localrobustness properties, which can provably eliminate classes of evasion attacksfor most inputs, but not all inputs. Since data distribution shift is verycommon in security applications, e.g., often observed for malware detection,local robustness cannot guarantee that the property holds for unseen inputs atthe time of deploying the classifier. Therefore, it is more desirable toenforce global robustness properties that hold for all inputs, which isstrictly stronger than local robustness.  In this paper, we present a framework and tools for training classifiers thatsatisfy global robustness properties. We define new notions of globalrobustness that are more suitable for security classifiers. We design a novelbooster-fixer training framework to enforce global robustness properties. Westructure our classifier as an ensemble of logic rules and design a newverifier to verify the properties. In our training algorithm, the boosterincreases the classifier's capacity, and the fixer enforces verified globalrobustness properties following counterexample guided inductive synthesis.  We show that we can train classifiers to satisfy different global robustnessproperties for three security datasets, and even multiple properties at thesame time, with modest impact on the classifier's performance. For example, wetrain a Twitter spam account classifier to satisfy five global robustnessproperties, with 5.4% decrease in true positive rate, and 0.1% increase infalse positive rate, compared to a baseline XGBoost model that doesn't satisfyany property.

Learning Security Classifiers with Verified Global Robustness Properties