Robustness Verification for Classifier Ensembles
This addresses the critical need for provable security in machine learning systems, particularly for safety-critical applications, though it is incremental as it builds on existing verification methods.
The authors tackled the problem of verifying robustness for classifier ensembles against randomized attacks, showing NP-hardness and providing SMT/MILP encodings to compute optimal attacks or prove robustness, with promising experimental results in scalability and applicability for image-classification tasks.
We give a formal verification procedure that decides whether a classifier ensemble is robust against arbitrary randomized attacks. Such attacks consist of a set of deterministic attacks and a distribution over this set. The robustness-checking problem consists of assessing, given a set of classifiers and a labelled data set, whether there exists a randomized attack that induces a certain expected loss against all classifiers. We show the NP-hardness of the problem and provide an upper bound on the number of attacks that is sufficient to form an optimal randomized attack. These results provide an effective way to reason about the robustness of a classifier ensemble. We provide SMT and MILP encodings to compute optimal randomized attacks or prove that there is no attack inducing a certain expected loss. In the latter case, the classifier ensemble is provably robust. Our prototype implementation verifies multiple neural-network ensembles trained for image-classification tasks. The experimental results using the MILP encoding are promising both in terms of scalability and the general applicability of our verification procedure.