def check_condition_rdp_gp(args, radius, sample_rate, steps, alpha, delta,
sigma, p1, p2):
if radius == 0:
return True
if args.train_mode == 'DP' or args.train_mode == 'Sub-DP-no-amp':
rdp = PrivacyEngine._get_renyi_divergence(sample_rate=sample_rate,
noise_multiplier=sigma,
alphas=[alpha]) * steps
eps = rdp.cpu().detach().numpy()[0]
elif args.train_mode == 'Sub-DP':
_, eps = rdp_amplify(alpha, args.sub_training_size, args.training_size,
sample_rate, sigma)
eps *= steps
alpha = alpha / radius
eps = 3**(np.log2(radius)) * eps
if alpha <= 1:
return False
val = np.e**(-eps) * p1**(alpha/(alpha-1)) - \
(np.e**eps * p2)**((alpha-1)/alpha)
if val > 0:
return True
else:
return False
def func(alpha):
rdp = PrivacyEngine._get_renyi_divergence(sample_rate=sample_rate,
noise_multiplier=sigma,
alphas=[alpha])
eps = rdp.cpu().detach().numpy()[0]
return eps
def rdp_bounds(radius,
sample_rate,
steps,
alpha,
sigma,
p1,
p2,
softmax,
agg_res_param=None,
amplify=False,
training_size=None,
sub_training_size=None,
clip=True):
sample_rate_gp = 1 - (1 - sample_rate)**radius
if not amplify:
rdp = PrivacyEngine._get_renyi_divergence(sample_rate=sample_rate_gp,
noise_multiplier=sigma,
alphas=[alpha]) * steps
eps = rdp.cpu().detach().numpy()[0]
else:
_, eps = rdp_amplify(alpha, sub_training_size, training_size,
sample_rate_gp, sigma)
eps *= steps
if not softmax:
lower = np.e**(-eps) * p1**(alpha / (alpha - 1))
upper = (np.e**eps * p2)**((alpha - 1) / alpha)
else:
if agg_res_param is not None:
mgf_diff_list, varis_p1, varis_p2 = agg_res_param[
'mgf_diff_list'], agg_res_param['varis_p1_p2'][
0], agg_res_param['varis_p1_p2'][1]
def moments(order, mean, varis):
from sympy import symbols
t, mu, sigma = symbols('t, mu, sigma')
return mgf_diff_list[order].evalf(subs={
t: 0,
mu: mean,
sigma: varis
})
a1a = (alpha - 1) / alpha
aa1 = round(alpha / (alpha - 1))
upper_moments = moments(aa1, p2, varis_p2)
upper = np.e**(eps * a1a) * upper_moments**a1a
lower = np.e**(-eps) * p1**aa1
# def moments_bounds(agg_res, order):
# agg_res_pow = np.power(agg_res, order)
# return single_ci(agg_res_pow, 1e-5)
# p1_agg_res = agg_res[:, p1_idx]
# p2_agg_res = agg_res[:, p2_idx]
# _, l1, _ = moments_bounds(p1_agg_res, (alpha-1)/alpha)
# _, _, u2 = moments_bounds(p2_agg_res, alpha/(alpha-1))
# if l1 == 1 or u2 == 0:
# p1_agg_res = np.longdouble(agg_res[:, p1_idx])
# p2_agg_res = np.longdouble(agg_res[:, p2_idx])
# _, l1, _ = moments_bounds(p1_agg_res, (alpha-1)/alpha)
# _, _, u2 = moments_bounds(p2_agg_res, alpha/(alpha-1))
# lower = np.e**(-eps) * l1**(alpha/(alpha-1))
# upper = (np.e**eps * u2)**((alpha-1)/alpha)
else:
lower = np.e**(-eps) * p1**(alpha / (alpha - 1))
upper = (np.e**eps * p2)**((alpha - 1) / alpha)
if clip:
return min(max(lower, 0), 1), max(min(upper, 1), 0)
else:
return lower, upper
