Does $\epsilon$-differential privacy treat databases with one record of difference a completely different databases?

Question

Does $\epsilon$-differential privacy treat databases with one record difference completely different database?

What I want to know is about continuous release. Suppose we have a set of users and some other guy outside the group (say analyst) gets aggregate result periodically. In order to obtain the $\epsilon$-DP in a central model, then what we need is adding appropriate noise to the result, and release it to the analyst. The problem of this approach is that as time continues (say infinity), the privacy loss gets infinity.

If the some users in the group get slightly different at a time (say, they gets permanently disappear or there are someones newly joining), is the privacy loss still accumulated? Is there any chance to refresh or rest the loss?

Thanks

Answer 1

is the privacy loss still accumulated?

Yes.

To prove $\epsilon$-differential privacy, it is assumed that the adversary has total knowledge of the database except for one record. For this record the adversary doesn't know if it is in the database or not. So if the database changes by adding or removing (other) records, the adversary would know that and would adjust his expectations accordingly. So for that one record for which the adversary doesn't know whether it is part of the database or not, the privacy loss still accumulates in a setting of continuous release.

In practice an adversary probably isn't that strong, and would have a harder time saying something useful about what he/she does or does not know. But $\epsilon$-differential isn't about guessing what an adversary can do, it's about mathematically proving what he cannot do.