Learning Security Classifiers with Verified Global Robustness Properties

Recent works have proposed methods to train classifiers with local robustness properties, which can provably eliminate classes of evasion attacks for most inputs, but not all inputs. Since data distribution shift is very common in security applications, e.g., often observed for malware detection, local robustness cannot guarantee that the property holds for unseen inputs at the time of deploying the classifier. Therefore, it is more desirable to enforce global robustness properties that hold for all inputs, which is strictly stronger than local robustness. In this paper, we present a framework and tools for training classifiers that satisfy global robustness properties. We define new notions of global robustness that are more suitable for security classifiers. We design a novel booster-fixer training framework to enforce global robustness properties. We structure our classifier as an ensemble of logic rules and design a new verifier to verify the properties. In our training algorithm, the booster increases the classifier's capacity, and the fixer enforces verified global robustness properties following counterexample guided inductive synthesis. To the best of our knowledge, the only global robustness property that has been previously achieved is monotonicity. Several previous works have defined global robustness properties, but their training techniques failed to achieve verified global robustness. In comparison, we show that we can train classifiers to satisfy different global robustness properties for three security datasets, and even multiple properties at the same time, with modest impact on the classifier's performance. For example, we train a Twitter spam account classifier to satisfy five global robustness properties, with 5.4% decrease in true positive rate, and 0.1% increase in false positive rate, compared to a baseline XGBoost model that doesn't satisfy any property.