PLDP-FL: Federated Learning with Personalized Local Differential Privacy

. 2023 Mar 10;25(3):485. doi: 10.3390/e25030485

Algorithm 2 PDPM

Require: The personalized privacy parameters

(τ_{i}, ϵ_{i})

, the range length of

τ_{i}

L_{i} = | τ_{i} |

, the midpoint of

τ_{i}

c_{i}

, and the client’s input value

w_{i} \in τ_{i}

.
Ensure: The value after perturbation

{\tilde{w}}_{i}

1:
if $c_{i} \neq 0$ then
2:
Translating $c_{i}$ to point 0 so that $τ_{i}$ is symmetric about point 0;
3:
$v_{i} = w_{i} - c_{i}$ ;
4:
else
5:
$v_{i} = w_{i}$ .
6:
end if
7:
Sampling a random variable a such that
8:
$P r [a = L_{i} / 2] = \frac{v_{i} (e^{ϵ_{i}} - 1)}{L_{i} (e^{ϵ_{i}} + 2)} + \frac{e^{ϵ_{i}} + 1}{2 (e^{ϵ_{i}} + 2)}$ ;
9:
if $a = L_{i} / 2$ then
10:
${\tilde{v}}_{i} = \frac{L_{i} (e^{ϵ_{i}} + 3)}{2 (e^{ϵ_{i}} - 1)}$ ;
11:
else if $a = - L_{i} / 2$ then
12:
${\tilde{v}}_{i} = - \frac{L_{i} (e^{ϵ_{i}} + 1)}{e^{ϵ_{i}} - 1}$ ;
13:
else
14:
${\tilde{v}}_{i} = 0$ ;
15:
end if
16:
${\tilde{w}}_{i} = {\tilde{v}}_{i} + c_{i}$ ;
17:
return ${\tilde{w}}_{i}$ .