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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))