def _apply_dp_sgd_analysis(
sample_rate: float,
noise_multiplier: float,
steps: int,
alphas: List[float],
delta: float,
verbose: bool = True,
) -> Tuple[float, float]:
"""
Performs the DP-SGD privacy analysis based on sample rate and steps.
Performs the DP-SGD privacy analysis and computes privacy loss epsilon
and optimal order alpha.
Parameters
----------
sample_rate : float
The sample rate in SGD
noise_multiplier : float
The ratio of the standard deviation of the Gaussian noise to
the L2-sensitivity of the function to which the noise is added
steps : int
The number of steps
alphas : List[float]
A list of RDP orders
delta : float
Target delta
verbose : bool, optional
If enabled, will print the results of DP-SGD analysis; by default True
Returns
-------
Tuple[float, float]
Pair of privacy loss epsilon and optimal order alpha
"""
rdp = tf_privacy.compute_rdp(sample_rate, noise_multiplier, steps, alphas)
eps, opt_alpha = tf_privacy.get_privacy_spent(alphas, rdp, delta=delta)
if verbose:
print(
f"DP-SGD with\n\tsampling rate = {100 * sample_rate:.3g}%,"
f"\n\tnoise_multiplier = {noise_multiplier},"
f"\n\titerated over {steps} steps,\nsatisfies "
f"differential privacy with\n\tepsilon = {eps:.3g},"
f"\n\tdelta = {delta}."
f"\nThe optimal alpha is {opt_alpha}."
)
if opt_alpha == max(alphas) or opt_alpha == min(alphas):
print(
"The privacy estimate is likely to be improved by expanding "
"the set of alpha orders."
)
return eps, opt_alpha
def test_privacy_analysis_example(self):
# IMPORTANT: When changing this code you also need to update
# the docstring for opacus.privacy_analysis module
parameters = [(1e-5, 1.0, 10), (1e-4, 3.0, 4)]
delta = 1e-5
max_order = 32
orders = range(2, max_order + 1)
rdp = np.zeros_like(orders, dtype=float)
for q, sigma, steps in parameters:
rdp += privacy_analysis.compute_rdp(q, sigma, steps, orders)
epsilon, opt_order = privacy_analysis.get_privacy_spent(orders, rdp, delta)
def _apply_dp_sgd_analysis(
sample_rate: float,
noise_multiplier: float,
steps: int,
alphas: List[float],
delta: float,
verbose: bool = True,
) -> Tuple[float, float]:
"""
Computes the privacy Epsilon at a given delta via RDP accounting and
converting to an (epsilon, delta) guarantee for a target Delta.
Args:
sample_rate : The sample rate in SGD
noise_multiplier : The ratio of the standard deviation of the Gaussian
noise to the L2-sensitivity of the function to which the noise is added
steps : The number of steps
alphas : A list of RDP orders
delta : Target delta
verbose : If enabled, will print the results of DP-SGD analysis
Returns:
Pair of privacy loss epsilon and optimal order alpha
"""
rdp = tf_privacy.compute_rdp(sample_rate, noise_multiplier, steps, alphas)
eps, opt_alpha = tf_privacy.get_privacy_spent(alphas, rdp, delta=delta)
if verbose:
print(
f"DP-SGD with\n\tsampling rate = {100 * sample_rate:.3g}%,"
f"\n\tnoise_multiplier = {noise_multiplier},"
f"\n\titerated over {steps} steps,\nsatisfies "
f"differential privacy with\n\tepsilon = {eps:.3g},"
f"\n\tdelta = {delta}."
f"\nThe optimal alpha is {opt_alpha}."
)
if opt_alpha == max(alphas) or opt_alpha == min(alphas):
print(
"The privacy estimate is likely to be improved by expanding "
"the set of alpha orders."
)
return eps, opt_alpha
def get_privacy_spent(total_rdp, target_delta=1e-5, orders=ORDERS):
return tf_privacy.get_privacy_spent(orders, total_rdp, target_delta)