Adaptive continual observation: extending privacy guarantees

Prove that the algorithms and guarantees presented for the non-adaptive continual observation model—specifically, the transformation BBRestrictedToNodePriv (Algorithm 5) together with the time-aware projections IIBBDS and IIDLL and their accuracy and privacy bounds—hold verbatim in the adaptive continual observation model of Jain et al. (JRSS23), in which inputs may depend on prior outputs.

Background

The paper defines and analyzes privacy under continual observation in the non-adaptive setting, where the entire input stream is fixed independently of the mechanism’s outputs. The core tools used—tree mechanisms and the sparse vector technique—are known to support adaptive privacy in prior work.

Motivated by this, the authors conjecture that their algorithms and analyses extend unchanged to the adaptive setting of JRSS23, but they do not provide a proof, leaving a formal extension as an open conjecture.