  Cloud service providers have launched Machine-Learning-as-a-Service (MLaaS)
platforms to allow users to access large-scale cloudbased models via APIs. In
addition to prediction outputs, these APIs can also provide other information
in a more human-understandable way, such as counterfactual explanations (CF).
However, such extra information inevitably causes the cloud models to be more
vulnerable to extraction attacks which aim to steal the internal functionality
of models in the cloud. Due to the black-box nature of cloud models, however, a
vast number of queries are inevitably required by existing attack strategies
before the substitute model achieves high fidelity. In this paper, we propose a
novel simple yet efficient querying strategy to greatly enhance the querying
efficiency to steal a classification model. This is motivated by our
observation that current querying strategies suffer from decision boundary
shift issue induced by taking far-distant queries and close-to-boundary CFs
into substitute model training. We then propose DualCF strategy to circumvent
the above issues, which is achieved by taking not only CF but also
counterfactual explanation of CF (CCF) as pairs of training samples for the
substitute model. Extensive and comprehensive experimental evaluations are
conducted on both synthetic and real-world datasets. The experimental results
favorably illustrate that DualCF can produce a high-fidelity model with fewer
queries efficiently and effectively.
