text: # 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, noise_lbd):
    """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 = noise_lbd  # minimum possible noise
    init_epsilon, _ = apply_dp_sgd_analysis(q, init_noise, steps, orders, delta)
  
    if init_epsilon < target_epsilon:  # noise_lbd was an overestimate
      print("min_noise too large for target epsilon.")
      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
  