Merge branch 'tensorflow:master' into master

tensorflow_privacy/privacy/analysis/BUILD

@@ -84,6 +84,7 @@ py_library(
     name = "tree_aggregation_accountant",
     srcs = ["tree_aggregation_accountant.py"],
     srcs_version = "PY3",
+    deps = ["@com_google_differential_py//dp_accounting:accounting"],
 )
 
 py_test(

tensorflow_privacy/privacy/analysis/tree_aggregation_accountant.py

@@ -69,8 +69,9 @@ appearance of a same sample. For `target_delta`, the estimated epsilon is:
 
 import functools
 import math
-from typing import Collection, Union
+from typing import Collection, Optional, Union
 
+import dp_accounting
 import numpy as np
 
 
@@ -376,3 +377,26 @@ def compute_zcdp_single_tree(
   sum_sensitivity_square = _max_tree_sensitivity_square_sum(
       max_participation, min_separation, total_steps)
   return _compute_gaussian_zcdp(noise_multiplier, sum_sensitivity_square)
+
+
+def _gaussian_zcdp_to_epsilon(
+    zcdp: float,
+    target_delta: float = 1e-10,
+    accountant: Optional[dp_accounting.PrivacyAccountant] = None,
+) -> float:
+  """Transforms zCDP of Gaussian Mechanism to (epsilon, delta)-DP.
+
+  Args:
+    zcdp: Input zCDP value.
+    target_delta: Specified target delta for (epsilon, delta)-DP.
+    accountant: Defaults to PLD accounting. Other options including RDP, i.e.,
+      dp_accounting.rdp.RdpAccountant()
+
+  Returns:
+    Epsilon under given delata for (epsilon, delta)-DP.
+  """
+  if accountant is None:
+    accountant = dp_accounting.pld.PLDAccountant()
+  noise_multiplier = 1.0 / (zcdp * 2) ** 0.5
+  accountant.compose(dp_accounting.GaussianDpEvent(noise_multiplier), 1)
+  return accountant.get_epsilon(target_delta)

tensorflow_privacy/privacy/analysis/tree_aggregation_accountant_test.py

@@ -187,6 +187,19 @@ class TreeAggregationTest(tf.test.TestCase, parameterized.TestCase):
             tree_aggregation_accountant._compute_gaussian_zcdp(
                 sigma, sum_sensitivity_square))
 
+  def test_gaussian_zcdp_to_epsilon(self):
+    # The example below is reported in
+    # https://ai.googleblog.com/2022/02/federated-learning-with-formal.html
+    # Uses updated default RDP order (i.e., orders=None) can achieve better
+    # guarantees. Uses PLD accounting (dp_accounting.pld.PLDAccountant) can
+    # usually be tigher than RDP.
+    zcdp = 0.81
+    orders = [1 + x / 10.0 for x in range(1, 100)] + list(range(12, 64))
+    eps = tree_aggregation_accountant._gaussian_zcdp_to_epsilon(
+        zcdp, accountant=dp_accounting.rdp.RdpAccountant(orders)
+    )
+    self.assertNear(eps, 8.92, err=0.01)
+
 
 if __name__ == '__main__':
   tf.test.main()