  The robustness of recommender systems has become a prominent topic within the
research community. Numerous adversarial attacks have been proposed, but most
of them rely on extensive prior knowledge, such as all the white-box attacks or
most of the black-box attacks which assume that certain external knowledge is
available. Among these attacks, the model extraction attack stands out as a
promising and practical method, involving training a surrogate model by
repeatedly querying the target model. However, there is a significant gap in
the existing literature when it comes to defending against model extraction
attacks on recommender systems. In this paper, we introduce Gradient-based
Ranking Optimization (GRO), which is the first defense strategy designed to
counter such attacks. We formalize the defense as an optimization problem,
aiming to minimize the loss of the protected target model while maximizing the
loss of the attacker's surrogate model. Since top-k ranking lists are
non-differentiable, we transform them into swap matrices which are instead
differentiable. These swap matrices serve as input to a student model that
emulates the surrogate model's behavior. By back-propagating the loss of the
student model, we obtain gradients for the swap matrices. These gradients are
used to compute a swap loss, which maximizes the loss of the student model. We
conducted experiments on three benchmark datasets to evaluate the performance
of GRO, and the results demonstrate its superior effectiveness in defending
against model extraction attacks.
