Generalised Likelihood Ratio Testing Adversaries through the Differential Privacy Lens

Differential Privacy (DP) provides tight upper bounds on the capabilities of optimal adversaries, but such adversaries are rarely encountered in practice. Under the hypothesis testing/membership inference interpretation of DP, we examine the Gaussian mechanism and relax the usual assumption of a Neyman-Pearson-Optimal (NPO) adversary to a Generalized Likelihood Test (GLRT) adversary. This mild relaxation leads to improved privacy guarantees, which we express in the spirit of Gaussian DP and $(\varepsilon, δ)$-DP, including composition and sub-sampling results. We evaluate our results numerically and find them to match the theoretical upper bounds.