Optimal adaptive covariance for deleted-record unlearning

Characterize the optimal variance for Gaussian continual unlearning mechanisms when their noise covariances can adapt to deleted records and preceding releases.

Background

The paper studies independent Gaussian noise and Gaussian random-walk noise for continual machine unlearning, with certification based on Gaussian differential privacy. Its covariance minimax results restrict attention to mechanisms whose joint noise covariance is fixed before any releases. Set-based random-walk noise can instead adapt its increment variances to the realized deleted sets and can outperform every fixed covariance by a factor of order $(\log M)^2$ on some data sequences.

The unresolved problem is to determine the optimal variance when covariance adaptation is permitted not only in response to deleted records but also to preceding releases. Solving it would extend the paper’s fixed-covariance minimax theory to adaptive covariance mechanisms.