Adding privacy analysis to the Logistic Regression for MNIST tutorial.

PiperOrigin-RevId: 254815428

tutorials/README.md

@@ -20,6 +20,10 @@ Here is a list of all the tutorials included:
 * `mnist_dpsgd_tutorial_keras.py`: learn a convolutional neural network on MNIST
   with differential privacy using tf.Keras.
 
+* `mnist_lr_tutorial.py`: learn a differentially private logistic regression
+  model on MNIST. The model illustrates application of the
+  "amplification-by-iteration" analysis (https://arxiv.org/abs/1808.06651).
+
 The rest of this README describes the different parameters used to configure
 DP-SGD as well as expected outputs for the `mnist_dpsgd_tutorial.py` tutorial.
 

tutorials/mnist_lr_tutorial.py

@@ -11,11 +11,10 @@
 # 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.
-
 """DP Logistic Regression on MNIST.
 
 DP Logistic Regression on MNIST with support for privacy-by-iteration analysis.
-Feldman, Vitaly, Ilya Mironov, Kunal Talwar, and Abhradeep Thakurta.
+Vitaly Feldman, Ilya Mironov, Kunal Talwar, and Abhradeep Thakurta.
 "Privacy amplification by iteration."
 In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS),
 pp. 521-532. IEEE, 2018.
@@ -36,6 +35,8 @@ from distutils.version import LooseVersion
 import numpy as np
 import tensorflow as tf
 
+from privacy.analysis.rdp_accountant import compute_rdp
+from privacy.analysis.rdp_accountant import get_privacy_spent
 from privacy.optimizers import dp_optimizer
 
 if LooseVersion(tf.__version__) < LooseVersion('2.0.0'):
@@ -45,32 +46,30 @@ else:
 
 FLAGS = flags.FLAGS
 
-flags.DEFINE_boolean('dpsgd', True, 'If True, train with DP-SGD. If False, '
-                     'train with vanilla SGD.')
+flags.DEFINE_boolean(
+    'dpsgd', True, 'If True, train with DP-SGD. If False, '
+    'train with vanilla SGD.')
 flags.DEFINE_float('learning_rate', 0.001, 'Learning rate for training')
-flags.DEFINE_float('noise_multiplier', 0.02,
+flags.DEFINE_float('noise_multiplier', 0.05,
                    'Ratio of the standard deviation to the clipping norm')
-flags.DEFINE_integer('batch_size', 1, 'Batch size')
+flags.DEFINE_integer('batch_size', 5, 'Batch size')
 flags.DEFINE_integer('epochs', 5, 'Number of epochs')
-flags.DEFINE_integer('microbatches', 1, 'Number of microbatches '
-                     '(must evenly divide batch_size)')
 flags.DEFINE_float('regularizer', 0, 'L2 regularizer coefficient')
 flags.DEFINE_string('model_dir', None, 'Model directory')
-flags.DEFINE_float('data_l2_norm', 8,
-                   'Bound on the L2 norm of normalized data.')
+flags.DEFINE_float('data_l2_norm', 8, 'Bound on the L2 norm of normalized data')
 
 
 def lr_model_fn(features, labels, mode, nclasses, dim):
   """Model function for logistic regression."""
   input_layer = tf.reshape(features['x'], tuple([-1]) + dim)
 
-  logits = tf.layers.dense(inputs=input_layer,
-                           units=nclasses,
-                           kernel_regularizer=tf.contrib.layers.l2_regularizer(
-                               scale=FLAGS.regularizer),
-                           bias_regularizer=tf.contrib.layers.l2_regularizer(
-                               scale=FLAGS.regularizer)
-                          )
+  logits = tf.layers.dense(
+      inputs=input_layer,
+      units=nclasses,
+      kernel_regularizer=tf.contrib.layers.l2_regularizer(
+          scale=FLAGS.regularizer),
+      bias_regularizer=tf.contrib.layers.l2_regularizer(
+          scale=FLAGS.regularizer))
 
   # Calculate loss as a vector (to support microbatches in DP-SGD).
   vector_loss = tf.nn.sparse_softmax_cross_entropy_with_logits(
@@ -80,18 +79,15 @@ def lr_model_fn(features, labels, mode, nclasses, dim):
 
   # Configure the training op (for TRAIN mode).
   if mode == tf.estimator.ModeKeys.TRAIN:
-
     if FLAGS.dpsgd:
-      # Use DP version of GradientDescentOptimizer. Other optimizers are
-      # available in dp_optimizer. Most optimizers inheriting from
-      # tf.train.Optimizer should be wrappable in differentially private
-      # counterparts by calling dp_optimizer.optimizer_from_args().
       # The loss function is L-Lipschitz with L = sqrt(2*(||x||^2 + 1)) where
       # ||x|| is the norm of the data.
+      # We don't use microbatches (thus speeding up computation), since no
+      # clipping is necessary due to data normalization.
       optimizer = dp_optimizer.DPGradientDescentGaussianOptimizer(
-          l2_norm_clip=math.sqrt(2*(FLAGS.data_l2_norm**2 + 1)),
+          l2_norm_clip=math.sqrt(2 * (FLAGS.data_l2_norm**2 + 1)),
           noise_multiplier=FLAGS.noise_multiplier,
-          num_microbatches=FLAGS.microbatches,
+          num_microbatches=1,
           learning_rate=FLAGS.learning_rate)
       opt_loss = vector_loss
     else:
@@ -103,21 +99,18 @@ def lr_model_fn(features, labels, mode, nclasses, dim):
     # the vector_loss because tf.estimator requires a scalar loss. This is only
     # used for evaluation and debugging by tf.estimator. The actual loss being
     # minimized is opt_loss defined above and passed to optimizer.minimize().
-    return tf.estimator.EstimatorSpec(mode=mode,
-                                      loss=scalar_loss,
-                                      train_op=train_op)
+    return tf.estimator.EstimatorSpec(
+        mode=mode, loss=scalar_loss, train_op=train_op)
 
   # Add evaluation metrics (for EVAL mode).
   elif mode == tf.estimator.ModeKeys.EVAL:
     eval_metric_ops = {
         'accuracy':
             tf.metrics.accuracy(
-                labels=labels,
-                predictions=tf.argmax(input=logits, axis=1))
+                labels=labels, predictions=tf.argmax(input=logits, axis=1))
     }
-    return tf.estimator.EstimatorSpec(mode=mode,
-                                      loss=scalar_loss,
-                                      eval_metric_ops=eval_metric_ops)
+    return tf.estimator.EstimatorSpec(
+        mode=mode, loss=scalar_loss, eval_metric_ops=eval_metric_ops)
 
 
 def normalize_data(data, data_l2_norm):
@@ -146,7 +139,7 @@ def load_mnist(data_l2_norm=float('inf')):
   train_data = train_data.reshape(train_data.shape[0], -1)
   test_data = test_data.reshape(test_data.shape[0], -1)
 
-  idx = np.random.permutation(len(train_data))   # shuffle data once
+  idx = np.random.permutation(len(train_data))  # shuffle data once
   train_data = train_data[idx]
   train_labels = train_labels[idx]
 
@@ -159,14 +152,50 @@ def load_mnist(data_l2_norm=float('inf')):
   return train_data, train_labels, test_data, test_labels
 
 
+def print_privacy_guarantees(epochs, batch_size, samples, noise_multiplier):
+  """Tabulating position-dependent privacy guarantees."""
+  if noise_multiplier == 0:
+    print('No differential privacy (additive noise is 0).')
+    return
+
+  print('In the conditions of Theorem 34 (https://arxiv.org/abs/1808.06651) '
+        'the training procedure results in the following privacy guarantees.')
+
+  print('Out of the total of {} samples:'.format(samples))
+
+  steps_per_epoch = samples // batch_size
+  orders = np.concatenate(
+      [np.linspace(2, 20, num=181),
+       np.linspace(20, 100, num=81)])
+  delta = 1e-5
+  for p in (.5, .9, .99):
+    steps = math.ceil(steps_per_epoch * p)  # Steps in the last epoch.
+    coef = 2 * (noise_multiplier * batch_size)**-2 * (
+        # Accounting for privacy loss
+        (epochs - 1) / steps_per_epoch +  # ... from all-but-last epochs
+        1 / (steps_per_epoch - steps + 1))  # ... due to the last epoch
+    # Using RDP accountant to compute eps. Doing computation analytically is
+    # an option.
+    rdp = [order * coef for order in orders]
+    eps, _, _ = get_privacy_spent(orders, rdp, target_delta=delta)
+    print('\t{:g}% enjoy at least ({:.2f}, {})-DP'.format(
+        p * 100, eps, delta))
+
+  # Compute privacy guarantees for the Sampled Gaussian Mechanism.
+  rdp_sgm = compute_rdp(batch_size / samples, noise_multiplier,
+                        epochs * steps_per_epoch, orders)
+  eps_sgm, _, _ = get_privacy_spent(orders, rdp_sgm, target_delta=delta)
+  print('By comparison, DP-SGD analysis for training done with the same '
+        'parameters and random shuffling in each epoch guarantees '
+        '({:.2f}, {})-DP for all samples.'.format(eps_sgm, delta))
+
+
 def main(unused_argv):
   tf.logging.set_verbosity(tf.logging.INFO)
-  if FLAGS.dpsgd and FLAGS.batch_size % FLAGS.microbatches != 0:
-    raise ValueError('Number of microbatches should divide evenly batch_size')
   if FLAGS.data_l2_norm <= 0:
-    raise ValueError('FLAGS.data_l2_norm needs to be positive.')
-  if FLAGS.learning_rate > 8 / FLAGS.data_l2_norm**2:
-    raise ValueError('The amplification by iteration analysis requires'
+    raise ValueError('data_l2_norm must be positive.')
+  if FLAGS.dpsgd and FLAGS.learning_rate > 8 / FLAGS.data_l2_norm**2:
+    raise ValueError('The amplification-by-iteration analysis requires'
                      'learning_rate <= 2 / beta, where beta is the smoothness'
                      'of the loss function and is upper bounded by ||x||^2 / 4'
                      'with ||x|| being the largest L2 norm of the samples.')
@@ -178,15 +207,12 @@ def main(unused_argv):
   train_data, train_labels, test_data, test_labels = load_mnist(
       data_l2_norm=FLAGS.data_l2_norm)
 
-  # Instantiate the tf.Estimator.
+  # Instantiate tf.Estimator.
   # pylint: disable=g-long-lambda
-  model_fn = lambda features, labels, mode: lr_model_fn(features, labels, mode,
-                                                        nclasses=10,
-                                                        dim=train_data.shape[1:]
-                                                       )
+  model_fn = lambda features, labels, mode: lr_model_fn(
+      features, labels, mode, nclasses=10, dim=train_data.shape[1:])
   mnist_classifier = tf.estimator.Estimator(
-      model_fn=model_fn,
-      model_dir=FLAGS.model_dir)
+      model_fn=model_fn, model_dir=FLAGS.model_dir)
 
   # Create tf.Estimator input functions for the training and test data.
   # To analyze the per-user privacy loss, we keep the same orders of samples in
@@ -198,22 +224,27 @@ def main(unused_argv):
       num_epochs=FLAGS.epochs,
       shuffle=False)
   eval_input_fn = tf.estimator.inputs.numpy_input_fn(
-      x={'x': test_data},
-      y=test_labels,
-      num_epochs=1,
-      shuffle=False)
+      x={'x': test_data}, y=test_labels, num_epochs=1, shuffle=False)
 
-  # Train the model
-  steps_per_epoch = train_data.shape[0] // FLAGS.batch_size
-  mnist_classifier.train(input_fn=train_input_fn,
-                         steps=steps_per_epoch * FLAGS.epochs)
+  # Train the model.
+  num_samples = train_data.shape[0]
+  steps_per_epoch = num_samples // FLAGS.batch_size
 
-  # Evaluate the model and print results
+  mnist_classifier.train(
+      input_fn=train_input_fn, steps=steps_per_epoch * FLAGS.epochs)
+
+  # Evaluate the model and print results.
   eval_results = mnist_classifier.evaluate(input_fn=eval_input_fn)
-  test_accuracy = eval_results['accuracy']
-  print('Test accuracy after %d epochs is: %.3f' % (FLAGS.epochs,
-                                                    test_accuracy))
+  print('Test accuracy after {} epochs is: {:.2f}'.format(
+      FLAGS.epochs, eval_results['accuracy']))
 
+  if FLAGS.dpsgd:
+    print_privacy_guarantees(
+        epochs=FLAGS.epochs,
+        batch_size=FLAGS.batch_size,
+        samples=num_samples,
+        noise_multiplier=FLAGS.noise_multiplier,
+    )
 
 if __name__ == '__main__':
   app.run(main)