add helper for computing noise_multiplier from epsilon

tensorflow_privacy/privacy/analysis/compute_noise_from_budget.py

@@ -0,0 +1,67 @@
+# Copyright 2019 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"""Command-line script for computing privacy of a model trained with DP-SGD.
+
+The script applies the RDP accountant to estimate privacy budget of an iterated
+Sampled Gaussian Mechanism. The mechanism's parameters are controlled by flags.
+
+Example:
+  compute_dp_sgd_privacy
+    --N=60000 \
+    --batch_size=256 \
+    --epsilon=2.92 \
+    --epochs=60 \
+    --delta=1e-5
+
+The output states that DP-SGD with these parameters should
+use a noise multiplier of 1.12.
+"""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import sys
+
+from absl import app
+from absl import flags
+
+from tensorflow_privacy.privacy.analysis.compute_noise_from_budget_lib import compute_noise
+
+# Opting out of loading all sibling packages and their dependencies.
+sys.skip_tf_privacy_import = True
+
+FLAGS = flags.FLAGS
+
+flags.DEFINE_integer('N', None, 'Total number of examples')
+flags.DEFINE_integer('batch_size', None, 'Batch size')
+flags.DEFINE_float('epsilon', None, 'Target epsilon for DP-SGD')
+flags.DEFINE_float('epochs', None, 'Number of epochs (may be fractional)')
+flags.DEFINE_float('delta', 1e-6, 'Target delta')
+
+
+def main(argv):
+  del argv  # argv is not used.
+
+  assert FLAGS.N is not None, 'Flag N is missing.'
+  assert FLAGS.batch_size is not None, 'Flag batch_size is missing.'
+  assert FLAGS.epsilon is not None, 'Flag epsilon is missing.'
+  assert FLAGS.epochs is not None, 'Flag epochs is missing.'
+  compute_noise(FLAGS.N, FLAGS.batch_size, FLAGS.epsilon,
+                FLAGS.epochs, FLAGS.delta)
+
+
+if __name__ == '__main__':
+  app.run(main)

tensorflow_privacy/privacy/analysis/compute_noise_from_budget_lib.py

@@ -0,0 +1,80 @@
+# Copyright 2019 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.
+# ==============================================================================
+"""Library for computing privacy values for DP-SGD."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import math
+import sys
+
+from absl import app
+from scipy.optimize import bisect
+
+from tensorflow_privacy.privacy.analysis.rdp_accountant import compute_rdp  # pylint: disable=g-import-not-at-top
+from tensorflow_privacy.privacy.analysis.rdp_accountant import get_privacy_spent
+
+# Opting out of loading all sibling packages and their dependencies.
+sys.skip_tf_privacy_import = True
+
+
+def apply_dp_sgd_analysis(q, sigma, steps, orders, delta):
+  """Compute and print results of DP-SGD analysis."""
+
+  # compute_rdp requires that sigma be the ratio of the standard deviation of
+  # the Gaussian noise to the l2-sensitivity of the function to which it is
+  # added. Hence, sigma here corresponds to the `noise_multiplier` parameter
+  # in the DP-SGD implementation found in privacy.optimizers.dp_optimizer
+  rdp = compute_rdp(q, sigma, steps, orders)
+
+  eps, _, opt_order = get_privacy_spent(orders, rdp, target_delta=delta)
+
+  return eps, opt_order
+
+
+def compute_noise(n, batch_size, target_epsilon, epochs, delta):
+  """Compute noise based on the given hyperparameters."""
+  q = batch_size / n  # q - the sampling ratio.
+  if q > 1:
+    raise app.UsageError('n must be larger than the batch size.')
+  orders = ([1.25, 1.5, 1.75, 2., 2.25, 2.5, 3., 3.5, 4., 4.5] +
+            list(range(5, 64)) + [128, 256, 512])
+  steps = int(math.ceil(epochs * n / batch_size))
+
+  init_noise = 1e-5  # minimum possible noise
+  init_epsilon, _ = apply_dp_sgd_analysis(q, init_noise, steps, orders, delta)
+
+  if init_epsilon < target_epsilon:  # 1e-5 was an overestimate
+    return 0
+
+  cur_epsilon = init_epsilon
+  max_noise, min_noise = init_noise, 0
+
+  # doubling to find the right range
+  while cur_epsilon > target_epsilon:  # until noise is large enough
+    max_noise, min_noise = max_noise*2, max_noise
+    cur_epsilon, _ = apply_dp_sgd_analysis(q, max_noise, steps, orders, delta)
+
+  def epsilon_fn(noise):  # should return 0 if guess_epsilon==target_epsilon
+    guess_epsilon = apply_dp_sgd_analysis(q, noise, steps, orders, delta)[0]
+    return guess_epsilon - target_epsilon
+
+  target_noise = bisect(epsilon_fn, min_noise, max_noise)
+  print('DP-SGD with sampling rate = {:.3g}% and noise_multiplier = {} iterated'
+        ' over {} steps satisfies'.format(100 * q, target_noise, steps), end=' ')
+  print('differential privacy with eps = {:.3g} and delta = {}.'.format(
+      target_epsilon, delta))
+  return target_noise

tensorflow_privacy/privacy/analysis/compute_noise_from_budget_test.py

@@ -0,0 +1,40 @@
+# Copyright 2019 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.
+# ==============================================================================
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+from absl.testing import absltest
+from absl.testing import parameterized
+
+from tensorflow_privacy.privacy.analysis import compute_noise_from_budget_lib
+
+
+class ComputeNoiseFromBudgetTest(parameterized.TestCase):
+
+  @parameterized.named_parameters(
+      ('Test0', 60000, 150, 0.941870567, 15, 1e-5, 1.3),
+      ('Test1', 100000, 100, 1.70928734, 30, 1e-7, 1.0),
+      ('Test2', 100000000, 1024, 5907984.81339406, 10, 1e-7, 0.1),
+  )
+  def test_compute_noise(self, n, batch_size, target_epsilon, epochs,
+                         delta, expected_noise):
+    target_noise = compute_noise_from_budget_lib.compute_noise(
+        n, batch_size, target_epsilon, epochs, delta)
+    self.assertAlmostEqual(target_noise, expected_noise)
+
+if __name__ == '__main__':
+  absltest.main()