def update_privacy_pars(priv_pars):
verify = False
max_lmbd = 32
lmbds = range(1, max_lmbd + 1)
log_moments = []
for lmbd in lmbds:
log_moment = 0
log_moment += gm.compute_log_moment(priv_pars['q'], priv_pars['sigma'], priv_pars['T'], lmbd, verify=verify)
log_moments.append((lmbd, log_moment))
priv_pars['eps'], _ = gm.get_privacy_spent(log_moments, target_delta=priv_pars['delta'])
return priv_pars
def moments_epsilon(target_delta, sigma, ratio, iterations):
#Gaussian_moments
max_lmbd = 32
lmbds = range(1, max_lmbd + 1)
eps_gm = []
log_moments = []
for lmbd in lmbds:
log_moment = gm.compute_log_moment(ratio, sigma, iterations, lmbd)
log_moments.append((lmbd, log_moment))
eps_e, delta_e = gm.get_privacy_spent(log_moments,
target_delta=target_delta)
eps_gm.append(eps_e)
print(eps_gm)
def ma(sigma, q, num_steps, delta, max_lamb=64):
max_moment_order = np.floor(-sigma**2 * np.log(q * sigma)).astype('int')
max_moment_order = min(max_moment_order, max_lamb)
assert q < 1 / (16 * sigma)
epsilon = np.inf
for lam in range(1, max_moment_order + 1):
try:
log_moment = compute_log_moment(q,
sigma,
num_steps,
lam,
verify=False)
eps = get_privacy_spent([(lam, log_moment)], target_delta=delta)[0]
epsilon = min(epsilon, eps)
except:
break
if eps == np.inf: break
return epsilon
def compute_epsilon(X, y, batch_size, sigma=4):
N, dim = X.shape
# sampling probability
q = batch_size / (N * 1.0)
# moments accountant
max_lmbd = 32
epsilon = []
T = [1, 10, 100, 1000]
delta = 1e-8
for niter in T:
log_moments = []
for lmbd in xrange(1, max_lmbd + 1):
log_moment = compute_log_moment(q, sigma, niter, lmbd)
log_moments.append((lmbd, log_moment))
eps, _ = get_privacy_spent(log_moments, target_delta=delta)
epsilon.append(eps)
return epsilon
def compare_accountants(totalexamples, group_size, iterations, sigma, delta):
itersinepoch = totalexamples // group_size
epochs = iterations // itersinepoch
q = float(group_size) / totalexamples
target_delta = delta
print((itersinepoch, epochs, q))
#linear composition
epsilon_linear = []
for k in [(x + 1) * itersinepoch for x in range(epochs)]:
delta_iter = target_delta / (k + 1) / q
epsilon_iter = math.sqrt(2.0 * math.log(1.25 / delta_iter)) / sigma
delta_iter_s = delta_iter * q #not used
epsilon_iter_s = math.log(1.0 + q * (math.exp(epsilon_iter) - 1.0))
epsilon_linear.append(k * epsilon_iter_s)
print("epsilon_linear", epsilon_linear)
#advanced composition
#each step is (q*epsilon, q*delta)-DP
#amplified privacy parameters with sampling ratio q
epsilon_adv = []
for k in [(x + 1) * itersinepoch for x in range(epochs)]:
delta_iter = target_delta / ((k + 1) * q)
# guassian mechanism
epsilon_iter = math.ceil(math.sqrt(
2.0 * math.log(1.25 / delta_iter))) / sigma
##under sampling
delta_iter_s = q * delta_iter
epsilon_iter_s = math.log(1.0 + q * (math.exp(epsilon_iter) - 1.0))
delta_prime = target_delta / (k + 1)
if (delta_prime <= 0):
print('delta_prime is not larger than 0 with %d' % k)
break
epsilon_e = epsilon_iter_s * math.sqrt(
2.0 * k * math.log(1.0 / delta_prime)) + k * epsilon_iter_s * (
math.exp(epsilon_iter_s) - 1.0)
delta_e = k * delta_iter_s + delta_prime #not used
epsilon_adv.append(epsilon_e)
#print([epsilon_iter_p*k, delta_iter_p*k])
print('epsilon_adv', epsilon_adv)
#dp learning's advance composition implementation
epsilon_adv = []
target_delta = delta
for k in [(x + 1) * itersinepoch for x in range(epochs)]:
# guassian mechanism
delta_iter = target_delta / q / k
epsilon_iter = math.sqrt(2.0 * math.log(1.25 / delta_iter)) / sigma
##under sampling
delta_iter_s = q * delta_iter
epsilon_iter_s = math.log(1.0 + q * (math.exp(epsilon_iter) - 1.0))
#print([epsilon_iter_p*k, delta_iter_p*k])
epsilon_adv.append(math.sqrt(k * epsilon_iter_s * epsilon_iter_s))
print('epsilon_adv_deep', epsilon_adv)
#Gaussian_moments
max_lmbd = 32
lmbds = range(1, max_lmbd + 1)
eps_gm = []
for k in [(x + 1) * itersinepoch for x in range(epochs)]:
log_moments = []
for lmbd in lmbds:
log_moment = gm.compute_log_moment(q, sigma, k, lmbd)
log_moments.append((lmbd, log_moment))
eps_e, delta_e = gm.get_privacy_spent(log_moments, target_delta=delta)
eps_gm.append(eps_e)
print('epsilon_MA', eps_gm)
#compute zCDP
eps_zcdp = []
rho_iter = 1.0 / (2.0 * sigma**2)
rho_e = rho_iter
for e in range(1, epochs + 1):
rho_c = rho_e * e
epsilon_e = rho_c + 2 * math.sqrt(rho_c * math.log(1 / delta))
eps_zcdp.append(epsilon_e)
print('epsilon_zCDP', eps_zcdp)
# compute zCDP with sampling--approximate bound 1
eps_zcdp_sampled = []
rho_iter = 1.0 / (2.0 * sigma**2) * q**2 / (1 - q)
rho_e = rho_iter * itersinepoch
for e in range(1, epochs + 1):
rho_c = rho_e * e
epsilon_e = (q**3) * itersinepoch * e + rho_c + 2 * math.sqrt(
rho_c * (math.log(1.0 / delta)))
eps_zcdp_sampled.append(epsilon_e)
print('epsilon_sampled_zCDP', eps_zcdp_sampled)
# compute zCDP with random sampling updated----approximate bound 2
eps_zcdp_sampled_v2 = []
rho_iter = 1.0 / (sigma**2) * q**2
rho_e = rho_iter * itersinepoch
for e in range(1, epochs + 1):
rho_c = rho_e * e
if (e < 10):
th = 1 / math.exp(rho_c * sigma**4 * (math.log(1 / q / sigma))**2)
if delta < th:
epsilon_e = rho_c * (
sigma**2 * math.log(1 / q / sigma) +
1) - math.log(delta) / sigma**2 / math.log(1 / q / sigma)
else:
epsilon_e = rho_c + 2 * math.sqrt(rho_c *
(math.log(1.0 / delta)))
else:
epsilon_e = rho_c + 2 * math.sqrt(rho_c * (math.log(1.0 / delta)))
eps_zcdp_sampled_v2.append(epsilon_e)
print('epsilon_sampled_zCDP_v2', eps_zcdp_sampled_v2)
return [epsilon_adv, eps_gm, eps_zcdp]
