Age-Dependent Differential Privacy

The proliferation of real-time applications has motivated extensive research on analyzing and optimizing data freshness in the context of age of information. However, classical frameworks of privacy (e.g., differential privacy (DP)) have overlooked the impact of data freshness on privacy guarantees, which may provide a new tool for time-varying databases. In this work, we introduce age-dependent DP, taking into account the underlying stochastic nature of a time-varying database. In this new framework, we assume knowledge of the data process's statistical information and establish a connection between classical DP and age-dependent DP. We use this connection to characterize the impact of data staleness and temporal correlation on privacy guarantees. Our characterization reveals that the total variation distance is the sole essential statistical information. Moreover, we demonstrate that aging, which involves utilizing stale data inputs and/or delaying the release of outputs, can serve as a novel strategy for safeguarding data privacy, in addition to the traditional approach of injecting noise in the DP framework. Furthermore, to generalize our results to a multi-query scenario, we present a sequential composition result for age-dependent DP under any publishing and aging policies. We then characterize the optimal tradeoffs between privacy risk and utility and show how this can be achieved. Finally, case studies show that to achieve an arbitrarily small privacy risk in a single-query case, combing aging and noise injection only leads to a bounded accuracy loss, whereas using noise injection only (as in the benchmark case of DP) will lead to an unbounded accuracy loss.