Private Vector Mean Estimation in the Shuffle Model: Optimal Rates Require Many Messages

1 Mins read

We study the problem of private vector mean estimation in the shuffle model of privacy where nn users each have a unit vector in dd dimensions. We propose a new multi-message protocol that achieves the optimal error using O~(min(nε2,d))\tilde{\mathcal{O}}\left(\min(n\varepsilon^2,d)\right)

Additionally, we study the single-message setting and design a protocol that achieves mean squared error O(dnd/(d+2)ε4/(d+2))\mathcal{O}(dn^{d/(d+2)}\varepsilon^{-4/(d+2)})

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