关于楼梯机制的对称性在各地不同隐私制度间不同隐私效率中的作用

On the role of symmetry for staircase mechanisms in local differential privacy efficiency across different privacy regimes

We investigate the structural foundations of statistical efficiency under $α$-local differential privacy, with a focus on maximizing Fisher information. Building on the role of continuous staircase mechanisms, we identify a fundamental symmetry regarding the extremal values $1$ and $e^α$. We demonstrate that when the optimal measure satisfies this symmetry, the Fisher information admits a closed-form expression. More generally, we derive a decomposition of the Fisher information into symmetric a