def policy_loss_coeff_advantage_indicator(
networks: CRRNetworks,
policy_params: networks_lib.Params,
critic_params: networks_lib.Params,
transition: types.Transition,
key: networks_lib.PRNGKey,
num_action_samples: int = 4) -> jnp.ndarray:
"""Indicator advantage weighting; see equation (3) in CRR paper."""
advantage = _compute_advantage(networks, policy_params, critic_params,
transition, key, num_action_samples)
return jnp.heaviside(advantage, 0.)
def step(x):
"""This is the unit step function, but the deriative is defined and equal to 0 at every point.
Parameters
----------
x : array-like
Array to apply step to.
Returns
-------
step_x : array-like
step(x)
"""
return np.heaviside(x, 0)
def relax_plus_rebar_objective(encoder_params,
decoder_params,
surrogate_params,
log_temperature,
batch,
prng_key,
num_samples=1):
"""
Computes the REBAR objective function of a discrete VAE.
:param encoder_params: encoder parameters (list)
:param decoder_params: decoder parameters (list)
:param surrogate_params: surrogate parameters (list)
:param log_temperature: log of inverse temperature
:param batch: batch of data (jax.numpy array)
:param prng_key: PRNG key
:param num_samples: number of samples
"""
temperature = np.exp(log_temperature)
def concrete(x):
return jax.nn.sigmoid(x * temperature)
encoder1, encoder2 = encoder
encoder_params1, encoder_params2 = encoder_params
decoder1, decoder2 = decoder
decoder_params1, decoder_params2 = decoder_params
# Sampling
sampling_key, control_variate_key = random.split(prng_key)
first_layer_sampling_key, second_layer_sampling_key = random.split(
sampling_key)
first_layer_control_variate_key, second_layer_control_variate_key = random.split(
control_variate_key)
# Outer Layer
first_layer_params = encoder1(encoder_params1, batch) # BxD
first_layer_relaxed_samples = binary_relaxed.sample(
first_layer_params, first_layer_sampling_key, num_samples)
first_layer_posterior_samples = np.heaviside(
first_layer_relaxed_samples, 0)
first_layer_conditional_relaxed_samples = binary_relaxed.conditional_sample(
first_layer_params, first_layer_posterior_samples,
first_layer_control_variate_key)
# Inner Layer
second_layer_params = encoder2(encoder_params2,
first_layer_posterior_samples)
second_layer_relaxed_samples = binary_relaxed.sample(
second_layer_params, second_layer_sampling_key, num_samples=1)[0,
...]
second_layer_posterior_samples = np.heaviside(
second_layer_relaxed_samples, 0)
second_layer_conditional_relaxed_samples = binary_relaxed.conditional_sample(
second_layer_params, second_layer_posterior_samples,
second_layer_control_variate_key)
# Inner layer posterior
log_posterior = np.sum(bernoulli.logpmf(second_layer_posterior_samples,
second_layer_params),
axis=(1, 2))
# Outer layer posterior
log_posterior += np.sum(vmap(bernoulli.logpmf, in_axes=(0, None))(
first_layer_posterior_samples, first_layer_params),
axis=(1, 2))
def elbo_samples(first_layer_samples,
second_layer_samples,
stop_grads=False):
# Inner layer prior
log_prior = np.sum(bernoulli.logpmf(
second_layer_samples,
decoder2(decoder_params2, first_layer_samples)),
axis=(1, 2)) # SxBxD
# Outer layer prior
log_prior += np.sum(vmap(bernoulli.logpmf, in_axes=(0, None))(
first_layer_samples, 0.5 * np.ones((batch.shape[0], 200))),
axis=(1, 2)) # SxBxD
if stop_grads:
# Inner layer posterior
log_posterior = np.sum(bernoulli.logpmf(
second_layer_samples,
lax.stop_gradient(second_layer_params)),
axis=(1, 2))
# Outer layer posterior
log_posterior += np.sum(vmap(
bernoulli.logpmf,
in_axes=(0, None))(first_layer_samples,
lax.stop_gradient(first_layer_params)),
axis=(1, 2))
else:
# Inner layer posterior
log_posterior = np.sum(bernoulli.logpmf(
second_layer_samples, second_layer_params),
axis=(1, 2))
# Outer layer posterior
log_posterior += np.sum(vmap(
bernoulli.logpmf, in_axes=(0, None))(first_layer_samples,
first_layer_params),
axis=(1, 2))
# Likelihood
log_likelihood = vmap(bernoulli_log_likelihood,
in_axes=(None, 0, None))(decoder_params1,
first_layer_samples,
batch)
elbo_samples = log_likelihood - log_posterior + log_prior
return elbo_samples
elbo_evaluation = elbo_samples(first_layer_posterior_samples,
second_layer_posterior_samples)
unconditional_evaluation = elbo_samples(
concrete(first_layer_relaxed_samples),
concrete(second_layer_relaxed_samples))
conditional_evaluation = elbo_samples(
concrete(first_layer_conditional_relaxed_samples),
concrete(second_layer_conditional_relaxed_samples))
frozen_conditional_evaluation = elbo_samples(
concrete(
lax.stop_gradient(first_layer_conditional_relaxed_samples)),
concrete(
lax.stop_gradient(second_layer_conditional_relaxed_samples)),
stop_grads=True)
relaxed_surrogate_inputs = np.concatenate(
[first_layer_relaxed_samples, second_layer_relaxed_samples],
axis=-1)
conditional_relaxed_surrogate_inputs = np.concatenate([
first_layer_conditional_relaxed_samples,
second_layer_conditional_relaxed_samples
],
axis=-1)
obj = (lax.stop_gradient(elbo_evaluation) -
frozen_conditional_evaluation -
np.sum(surrogate(
surrogate_params,
lax.stop_gradient(conditional_relaxed_surrogate_inputs)),
axis=1).squeeze()) * log_posterior
obj += unconditional_evaluation + np.sum(surrogate(
surrogate_params, relaxed_surrogate_inputs),
axis=1).squeeze()
obj -= conditional_evaluation + np.sum(surrogate(
surrogate_params, conditional_relaxed_surrogate_inputs),
axis=1).squeeze()
return -np.mean(obj, axis=0) / batch.shape[0]
def tunable_rebar_objective(encoder_params,
decoder_params,
batch,
prng_key,
cv_coeff=1.0,
log_temperature=0.5,
num_samples=1):
"""
Computes the REBAR objective function of a discrete VAE.
:param encoder_params: encoder parameters (list)
:param decoder_params: decoder parameters (list)
:param batch: batch of data (jax.numpy array)
:param prng_key: PRNG key
:param cv_coeff: control variate coefficient
:param log_temperature: log_temperature parameter for rebar control variate.
:param num_samples: number of samples
"""
temperature = np.exp(log_temperature)
encoder1, encoder2 = encoder
encoder_params1, encoder_params2 = encoder_params
decoder1, decoder2 = decoder
decoder_params1, decoder_params2 = decoder_params
# Sampling
sampling_key, control_variate_key = random.split(prng_key)
first_layer_sampling_key, second_layer_sampling_key = random.split(
sampling_key)
first_layer_control_variate_key, second_layer_control_variate_key = random.split(
control_variate_key)
# Outer Layer
first_layer_params = encoder1(encoder_params1, batch) # BxD
first_layer_relaxed_samples = binary_relaxed.sample(
first_layer_params, first_layer_sampling_key, num_samples)
first_layer_posterior_samples = np.heaviside(
first_layer_relaxed_samples, 0)
first_layer_concrete_samples = jax.nn.sigmoid(
first_layer_relaxed_samples * temperature)
first_layer_conditional_relaxed_samples = binary_relaxed.conditional_sample(
first_layer_params, first_layer_posterior_samples,
first_layer_control_variate_key)
first_layer_cv_samples = jax.nn.sigmoid(
first_layer_conditional_relaxed_samples * temperature)
first_layer_frozen_cv_samples = jax.nn.sigmoid(
lax.stop_gradient(first_layer_conditional_relaxed_samples) *
temperature)
# Inner Layer
second_layer_params = encoder2(encoder_params2,
first_layer_posterior_samples)
second_layer_relaxed_samples = binary_relaxed.sample(
second_layer_params, second_layer_sampling_key, num_samples=1)[0,
...]
second_layer_posterior_samples = np.heaviside(
second_layer_relaxed_samples, 0)
second_layer_concrete_samples = jax.nn.sigmoid(
second_layer_relaxed_samples * temperature)
second_layer_conditional_relaxed_samples = binary_relaxed.conditional_sample(
second_layer_params, second_layer_posterior_samples,
second_layer_control_variate_key)
second_layer_cv_samples = jax.nn.sigmoid(
second_layer_conditional_relaxed_samples * temperature)
second_layer_frozen_cv_samples = jax.nn.sigmoid(
lax.stop_gradient(second_layer_conditional_relaxed_samples) *
temperature)
# Inner layer posterior
log_posterior = np.sum(bernoulli.logpmf(second_layer_posterior_samples,
second_layer_params),
axis=(1, 2))
# Outer layer posterior
log_posterior += np.sum(vmap(bernoulli.logpmf, in_axes=(0, None))(
first_layer_posterior_samples, first_layer_params),
axis=(1, 2))
def elbo_samples(first_layer_samples,
second_layer_samples,
stop_grads=False):
# Inner layer prior
log_prior = np.sum(bernoulli.logpmf(
second_layer_samples,
decoder2(decoder_params2, first_layer_samples)),
axis=(1, 2)) # SxBxD
# Outer layer prior
log_prior += np.sum(vmap(bernoulli.logpmf, in_axes=(0, None))(
first_layer_samples, 0.5 * np.ones((batch.shape[0], 200))),
axis=(1, 2)) # SxBxD
if stop_grads:
# Inner layer posterior
log_posterior = np.sum(bernoulli.logpmf(
second_layer_samples,
lax.stop_gradient(second_layer_params)),
axis=(1, 2))
# Outer layer posterior
log_posterior += np.sum(vmap(
bernoulli.logpmf,
in_axes=(0, None))(first_layer_samples,
lax.stop_gradient(first_layer_params)),
axis=(1, 2))
else:
# Inner layer posterior
log_posterior = np.sum(bernoulli.logpmf(
second_layer_samples, second_layer_params),
axis=(1, 2))
# Outer layer posterior
log_posterior += np.sum(vmap(
bernoulli.logpmf, in_axes=(0, None))(first_layer_samples,
first_layer_params),
axis=(1, 2))
# Likelihood
log_likelihood = vmap(bernoulli_log_likelihood,
in_axes=(None, 0, None))(decoder_params1,
first_layer_samples,
batch)
elbo_samples = log_likelihood - log_posterior + log_prior
return elbo_samples
elbo_evaluation = elbo_samples(first_layer_posterior_samples,
second_layer_posterior_samples)
concrete_evaluation = elbo_samples(first_layer_concrete_samples,
second_layer_concrete_samples)
cv_evaluation = elbo_samples(first_layer_cv_samples,
second_layer_cv_samples)
frozen_cv_evaluation = elbo_samples(first_layer_frozen_cv_samples,
second_layer_frozen_cv_samples,
True)
obj = (lax.stop_gradient(elbo_evaluation) -
cv_coeff * frozen_cv_evaluation) * log_posterior
obj += cv_coeff * (concrete_evaluation - cv_evaluation)
return -np.mean(obj, axis=0) / batch.shape[0]
def heaviside(x1, x2): if isinstance(x1, JaxArray): x1 = x1.value if isinstance(x2, JaxArray): x2 = x2.value return JaxArray(jnp.heaviside(x1, x2))
def relax_plus_rebar_objective(encoder_params,
decoder_params,
surrogate_params,
log_temperature,
batch,
prng_key,
num_samples=1):
"""
Computes the REBAR objective function of a discrete VAE.
:param encoder_params: encoder parameters (list)
:param decoder_params: decoder parameters (list)
:param surrogate_params: surrogate parameters (list)
:param log_temperature: log of inverse temperature
:param batch: batch of data (jax.numpy array)
:param prng_key: PRNG key
:param num_samples: number of samples
"""
temperature = np.exp(log_temperature)
def concrete(x):
return jax.nn.sigmoid(x * temperature)
posterior_params = encoder(encoder_params, batch) # BxD
# Sampling
sampling_key, conditional_sampling_key = random.split(prng_key)
# posterior_samples = bernoulli.sample(posterior_params, sampling_key, num_samples)
unconditional_samples = binary_relaxed.sample(posterior_params,
sampling_key,
num_samples)
posterior_samples = np.heaviside(unconditional_samples, 0)
conditional_samples = binary_relaxed.conditional_sample(
posterior_params, posterior_samples, conditional_sampling_key)
log_posterior = np.sum(vmap(bernoulli.logpmf,
in_axes=(0, None))(posterior_samples,
posterior_params),
axis=(1, 2))
def elbo_samples(samples, stop_grads=False):
log_prior = np.sum(vmap(bernoulli.logpmf, in_axes=(0, None))(
samples, 0.5 * np.ones(
(batch.shape[0], posterior_params.shape[-1]))),
axis=(1, 2)) # SxBxD
if stop_grads:
log_posterior = np.sum(vmap(
bernoulli.logpmf,
in_axes=(0, None))(samples,
lax.stop_gradient(posterior_params)),
axis=(1, 2))
else:
log_posterior = np.sum(vmap(bernoulli.logpmf,
in_axes=(0,
None))(samples,
posterior_params),
axis=(1, 2))
log_likelihood = vmap(bernoulli_log_likelihood,
in_axes=(None, 0, None))(decoder_params,
samples, batch)
elbo_samples = log_likelihood - log_posterior + log_prior
return elbo_samples
elbo_evaluation = elbo_samples(posterior_samples)
unconditional_evaluation = elbo_samples(
concrete(unconditional_samples))
conditional_evaluation = elbo_samples(concrete(conditional_samples))
frozen_conditional_evaluation = elbo_samples(
concrete(lax.stop_gradient(conditional_samples)), True)
obj = (lax.stop_gradient(elbo_evaluation) -
frozen_conditional_evaluation -
np.sum(surrogate(surrogate_params,
lax.stop_gradient(conditional_samples)),
axis=1).squeeze()) * log_posterior
obj += unconditional_evaluation + np.sum(surrogate(
surrogate_params, unconditional_samples),
axis=1).squeeze()
obj -= conditional_evaluation + np.sum(surrogate(
surrogate_params, conditional_samples),
axis=1).squeeze()
return -np.mean(obj, axis=0) / batch.shape[0]
def relax_objective(encoder_params,
decoder_params,
surrogate_params,
batch,
prng_key,
num_samples=1):
"""
Computes the REBAR objective function of a discrete VAE.
:param encoder_params: encoder parameters (list)
:param decoder_params: decoder parameters (list)
:param surrogate_params: surrogate parameters (list)
:param batch: batch of data (jax.numpy array)
:param prng_key: PRNG key
:param num_samples: number of samples
"""
posterior_params = encoder(encoder_params, batch) # BxD
# Sampling
sampling_key, conditional_sampling_key = random.split(prng_key)
# posterior_samples = bernoulli.sample(posterior_params, sampling_key, num_samples)
unconditional_samples = binary_relaxed.sample(posterior_params,
sampling_key,
num_samples)
posterior_samples = np.heaviside(unconditional_samples, 0)
conditional_samples = binary_relaxed.conditional_sample(
posterior_params, posterior_samples, conditional_sampling_key)
log_posterior = np.sum(vmap(bernoulli.logpmf,
in_axes=(0, None))(posterior_samples,
posterior_params),
axis=(1, 2))
def elbo_samples(samples):
log_prior = np.sum(vmap(bernoulli.logpmf, in_axes=(0, None))(
samples, 0.5 * np.ones(
(batch.shape[0], posterior_params.shape[-1]))),
axis=(1, 2)) # SxBxD
log_posterior = np.sum(vmap(bernoulli.logpmf,
in_axes=(0, None))(samples,
posterior_params),
axis=(1, 2))
log_likelihood = vmap(bernoulli_log_likelihood,
in_axes=(None, 0, None))(decoder_params,
samples, batch)
elbo_samples = log_likelihood - log_posterior + log_prior
return elbo_samples
elbo_evaluation = elbo_samples(posterior_samples)
obj = (lax.stop_gradient(elbo_evaluation) -
np.sum(surrogate(surrogate_params,
lax.stop_gradient(conditional_samples)),
axis=1).squeeze()) * log_posterior
obj += np.sum(surrogate(surrogate_params, unconditional_samples) -
surrogate(surrogate_params, conditional_samples),
axis=1).squeeze()
return -np.mean(obj, axis=0) / batch.shape[0]
def tunable_rebar_objective(encoder_params,
decoder_params,
batch,
prng_key,
cv_coeff=1.0,
log_temperature=0.5,
num_samples=1):
"""
Computes the REBAR objective function of a discrete VAE.
:param encoder_params: encoder parameters (list)
:param decoder_params: decoder parameters (list)
:param batch: batch of data (jax.numpy array)
:param prng_key: PRNG key
:param cv_coeff: control variate coefficient
:param log_temperature: log_temperature parameter for rebar control variate.
:param num_samples: number of samples
"""
temperature = np.exp(log_temperature)
posterior_params = encoder(encoder_params, batch) # BxD
def concrete(x):
return jax.nn.sigmoid(x * temperature)
# Sampling
sampling_key, control_variate_key = random.split(prng_key)
# posterior_samples = bernoulli.sample(posterior_params, sampling_key, num_samples)
relaxed_samples = binary_relaxed.sample(posterior_params, sampling_key,
num_samples)
posterior_samples = np.heaviside(relaxed_samples, 0)
# concrete_samples = jax.nn.sigmoid(relaxed_samples * temperature)
conditional_relaxed_samples = binary_relaxed.conditional_sample(
posterior_params, posterior_samples, control_variate_key)
# cv_samples = jax.nn.sigmoid(conditional_relaxed_samples * temperature)
# frozen_cv_samples = binary_relaxed.conditional_sample(lax.stop_gradient(posterior_params), posterior_samples,
# control_variate_key)
# frozen_cv_samples = jax.nn.sigmoid(lax.stop_gradient(conditional_relaxed_samples) * temperature)
log_posterior = np.sum(vmap(bernoulli.logpmf,
in_axes=(0, None))(posterior_samples,
posterior_params),
axis=(1, 2))
def elbo_samples(samples, stop_grads=False):
log_prior = np.sum(vmap(bernoulli.logpmf, in_axes=(0, None))(
samples, 0.5 * np.ones(
(batch.shape[0], posterior_params.shape[-1]))),
axis=(1, 2)) # SxBxD
if stop_grads:
log_posterior = np.sum(vmap(
bernoulli.logpmf,
in_axes=(0, None))(samples,
lax.stop_gradient(posterior_params)),
axis=(1, 2))
else:
log_posterior = np.sum(vmap(bernoulli.logpmf,
in_axes=(0,
None))(samples,
posterior_params),
axis=(1, 2))
log_likelihood = vmap(bernoulli_log_likelihood,
in_axes=(None, 0, None))(decoder_params,
samples, batch)
elbo_samples = log_likelihood - log_posterior + log_prior
return elbo_samples
elbo_evaluation = elbo_samples(posterior_samples)
concrete_evaluation = elbo_samples(concrete(relaxed_samples))
cv_evaluation = elbo_samples((concrete(conditional_relaxed_samples)))
frozen_cv_evaluation = elbo_samples(
concrete(lax.stop_gradient(conditional_relaxed_samples)), True)
obj = (lax.stop_gradient(elbo_evaluation) -
cv_coeff * frozen_cv_evaluation) * log_posterior
obj += cv_coeff * (concrete_evaluation - cv_evaluation)
return -np.mean(obj, axis=0) / batch.shape[0]
def f(x):
return np.heaviside(x, 0.5)[0]
def To(xi,const):
return np.heaviside(-(xi['beta']-np.pi),0.)*To1(xi,const)+np.heaviside(xi['beta']-np.pi,1.)*To2(xi,const)