Computationally efficient private algorithms for subspace learning

Construct computationally efficient differentially private algorithms for learning indicators of linear subspaces over an arbitrary field with sample complexity having linear dependence on the target subspace dimension.

Background

The paper establishes a sample-complexity bound with linear dependence on the maximum subspace dimension for private learning of subspace indicators, independent of the ambient dimension. However, the construction is not claimed to be computationally efficient.

The cited prior work posed closing the computational gap as part of its open question. The paper explicitly states that its result resolves the sample-complexity aspect but leaves the computational-efficiency requirement unresolved.

References

Their open question also asks for computationally efficient algorithms; our result does not settle that additional requirement.

— Nearly Linear Private Learning of Littlestone Classes  (2610.23160 - Moran et al., 16 Oct 2026) in Section 3, subsection “Subspaces: Codimension as Rank”