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We study design of black-box model extraction attacks that can send minimalnumber of queries from a publicly available dataset to a target ML modelthrough a predictive API with an aim to create an informative anddistributionally equivalent replica of the target. First, we definedistributionally equivalent and Max-Information model extraction attacks, andreduce them into a variational optimisation problem. The attacker sequentiallysolves this optimisation problem to select the most informative queries thatsimultaneously maximise the entropy and reduce the mismatch between the targetand the stolen models. This leads to an active sampling-based query selectionalgorithm, Marich, which is model-oblivious. Then, we evaluate Marich ondifferent text and image data sets, and different models, including CNNs andBERT. Marich extracts models that achieve $\sim 60-95\%$ of true model'saccuracy and uses $\sim 1,000 - 8,500$ queries from the publicly availabledatasets, which are different from the private training datasets. Modelsextracted by Marich yield prediction distributions, which are $\sim 2-4\times$closer to the target's distribution in comparison to the existing activesampling-based attacks. The extracted models also lead to $84-96\%$ accuracyunder membership inference attacks. Experimental results validate that Marichis query-efficient, and capable of performing task-accurate, high-fidelity, andinformative model extraction.

Marich: A Query-efficient Distributionally Equivalent Model Extraction Attack using Public Data