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tensorflow_privacy/privacy/analysis/GDprivacy_accountants.py
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# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# =============================================================================
r"""This code applies the Dual and Central Limit
Theorem (CLT) to estimate privacy budget of an iterated subsampled
Gaussian Mechanism (by either uniform or Poisson subsampling).
"""
import numpy as np
from scipy.stats import norm
from scipy import optimize
# Total number of examples:N
# batch size:batch_size
# Noise multiplier for DP-SGD/DP-Adam:noise_multiplier
# current epoch:epoch
# Target delta:delta
# Compute mu from uniform subsampling
def compute_muU(epoch,noise_multi,N,batch_size):
T=epoch*N/batch_size
c=batch_size*np.sqrt(T)/N
return(np.sqrt(2)*c*np.sqrt(np.exp(noise_multi**(-2))*norm.cdf(1.5/noise_multi)+3*norm.cdf(-0.5/noise_multi)-2))
# Compute mu from Poisson subsampling
def compute_muP(epoch,noise_multi,N,batch_size):
T=epoch*N/batch_size
return(np.sqrt(np.exp(noise_multi**(-2))-1)*np.sqrt(T)*batch_size/N)
# Dual between mu-GDP and (epsilon,delta)-DP
def delta_eps_mu(eps,mu):
return norm.cdf(-eps/mu+mu/2)-np.exp(eps)*norm.cdf(-eps/mu-mu/2)
# inverse Dual
def eps_from_mu(mu,delta):
def f(x):
return delta_eps_mu(x,mu)-delta
return optimize.root_scalar(f, bracket=[0, 500], method='brentq').root
# inverse Dual of uniform subsampling
def compute_epsU(epoch,noise_multi,N,batch_size,delta):
return(eps_from_mu(compute_muU(epoch,noise_multi,N,batch_size),delta))
# inverse Dual of Poisson subsampling
def compute_epsP(epoch,noise_multi,N,batch_size,delta):
return(eps_from_mu(compute_muP(epoch,noise_multi,N,batch_size),delta))