restricted prior is not picklable

[danielmk]

Describe the bug
Neither the restriction estimator nor the restricted prior are picklable. The issue has come up here before #790 and I opened a discussion #973

Trying to pickle the restriction estimator raises AttributeError: Can't pickle local object 'build_classifier.<locals>.build_nn'

Trying to pickle the restricted prior raises AttributeError: Can't pickle local object 'get_classifier_thresholder.<locals>.classifier_thresholder'

To Reproduce
Python 3.9.18 and SBI 0.22.0

This is the example code copied from handling invalid simulations plus pickle and os.

from sbi.inference import SNPE, simulate_for_sbi
from sbi.utils import RestrictionEstimator, BoxUniform
from sbi.analysis import pairplot
import torch
import os
import pickle

_ = torch.manual_seed(2)

def simulator(theta):
    perturbed_theta = theta + 0.5 * torch.randn(2)
    perturbed_theta[theta[:, 0] < 0.0] = torch.as_tensor([float("nan"), float("nan")])
    return perturbed_theta

prior = BoxUniform(-2 * torch.ones(2), 2 * torch.ones(2))

theta, x = simulate_for_sbi(simulator, prior, 1000)
print("Simulation outputs: ", x)

restriction_estimator = RestrictionEstimator(prior=prior)

restriction_estimator.append_simulations(theta, x)
classifier = restriction_estimator.train()

restricted_prior = restriction_estimator.restrict_prior()
samples = restricted_prior.sample((10_000,))
_ = pairplot(samples, limits=[[-2, 2], [-2, 2]], fig_size=(4, 4))

new_theta, new_x = simulate_for_sbi(simulator, restricted_prior, 1000)
print("Simulation outputs: ", new_x)

restriction_estimator.append_simulations(
    new_theta, new_x
)  # Gather the new simulations in the `restriction_estimator`.
(
    all_theta,
    all_x,
    _,
) = restriction_estimator.get_simulations()  # Get all simulations run so far.

inference = SNPE(prior=prior)
density_estimator = inference.append_simulations(all_theta, all_x).train()
posterior = inference.build_posterior()

posterior_samples = posterior.sample((10_000,), x=torch.ones(2))
_ = pairplot(posterior_samples, limits=[[-2, 2], [-2, 2]], fig_size=(3, 3))

dirname = os.path.dirname(__file__)

with open(os.path.join(dirname, 'restriction_estimator.pickle'), 'wb') as f:
    # Pickle the 'data' dictionary using the highest protocol available.
    pickle.dump(restriction_estimator, f, pickle.HIGHEST_PROTOCOL)

Error Message:
AttributeError: Can't pickle local object 'build_classifier.<locals>.build_nn'

Expected behavior
Should create the pickle file without error.

Additional context
I suspect the problem has to do with nested functions but I will look into it. I will provide a PR according to contribution guidelines where the restriction_estimator is picklable and the above script generates otherwise the same inference and restriction estimator.