Dimension Reduction via Random Projection for Privacy in Multi-Agent Systems

In a Multi-Agent System (MAS), individual agents observe various aspects of the environment and transmit this information to a central entity responsible for aggregating the data and deducing system parameters. To improve overall efficiency, agents may append certain private parameters to their observations. For example, in a crowd-sourced traffic monitoring system, commuters might share not only their current speed, but also sensitive information such as their location to enable more accurate route prediction. However, sharing such data can allow the central entity or a potential adversary to infer private details about the user, such as their daily routines. To mitigate these privacy risks, the agents sanitize the data before transmission. This sanitization inevitably results in a loss of utility. In this work, we formulate the problem as a utility-privacy trade-off and propose a novel compression-based approach leveraging the notion of robust concepts to sanitize the shared data. We further derive a bound on the norm of the compression matrix required to ensure maximal privacy while satisfying predefined utility constraints.