Private Means and the Curious Incident of the Free Lunch

We show that the most well-known and fundamental building blocks of DP implementations -- sum, mean, count (and many other linear queries) -- can be released with substantially reduced noise for the same privacy guarantee. We achieve this by projecting individual data with worst-case sensitivity $R$ onto a simplex where all data now has a constant norm $R$. In this simplex, additional ``free'' queries can be run that are already covered by the privacy-loss of the original budgeted query, and which algebraically give additional estimates of counts or sums.

@article{fitzsimons2025_2408.10438,
  title={ Private Means and the Curious Incident of the Free Lunch },
  author={ Jack Fitzsimons and James Honaker and Michael Shoemate and Vikrant Singhal },
  journal={arXiv preprint arXiv:2408.10438},
  year={ 2025 }
}