Robustness Verification for Classifier Ensembles

Robustness Verification for Classifier Ensembles

Gross, D.
Jansen, N.
Perez, G.A.
Raaijmakers, S.

Sokolsky, D.V. (editor)
Hung, O. (editor)

2020

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.

Adversarial attacks
Ensemble classifiers
Robustness
Encoding (symbols)
Formal verification
Integer programming
NP-hard
Classifier ensembles
Data set
Encodings
Expected loss
Formal verification procedures
Multiple neural networks
Prototype implementations
Upper Bound
Classification (of information)

http://resolver.tudelft.nl/uuid:493ca34d-7b37-4cbb-aba2-14e2af00a856

https://doi.org/10.1007/978-3-030-59152-6_15

955374

Springer, Cham

9783030591519

0302-9743

Automated Technology for Verification and Analysis. ATVA 2020. Lecture Notes in Computer Science Automated Technology for Verification and Analysis. ATVA 2020. Lecture Notes in Computer Science, 12302 (12302), 271-287

conference paper