Lagrangian Deep Learning for Private RIS-aided Localization: An Active Sensing Approach

In this paper, we study user localization in the presence of adversarial position estimation. In particular, we consider a point-to-point legitimate system incorporating a Reconfigurable Intelligent Surface (RIS), within an uncertainty region of it lies an eavesdropper (Eve). Our objective is to design an RIS phase configuration control policy that enhances legitimate user localization while degrading Eve's capability to accurately estimate this position. To this end, we propose a novel primal-dual optimization framework for training RIS controllers based on recurrent neural networks. Our numerical investigations showcase that the proposed method nearly matches the performance of advanced RIS phase configuration schemes that disregard Eve, while also satisfying privacy localization constraints.