def get_fullbatch_average(
dataset: OffpolicyDataset,
limit: Optional[int] = None,
by_steps: bool = True,
truncate_episode_at: Optional[int] = None,
reward_fn: Callable = None,
weight_fn: Callable = None,
gamma: Union[float, tf.Tensor] = 1.0) -> Union[float, tf.Tensor]:
"""Computes average reward over full dataset.
Args:
dataset: The dataset to sample experience from.
limit: If specified, the maximum number of steps/episodes to take from the
dataset.
by_steps: Whether to sample batches of steps (default) or episodes.
truncate_episode_at: If sampling by episodes, where to truncate episodes
from the environment, if at all.
reward_fn: A function that takes in an EnvStep and returns the reward for
that step. If not specified, defaults to just EnvStep.reward. When
sampling by episode, valid_steps is also passed into reward_fn.
weight_fn: A function that takes in an EnvStep and returns a weight for
that step. If not specified, defaults to gamma ** step_num. When
sampling by episode, valid_steps is also passed into reward_fn.
gamma: The discount factor to use for the default reward/weight functions.
Returns:
An estimate of the average reward.
"""
if reward_fn is None:
if by_steps:
reward_fn = _default_by_steps_reward_fn
else:
reward_fn = lambda *args: _default_by_episodes_reward_fn(
*args, gamma=gamma)
if weight_fn is None:
if by_steps:
weight_fn = lambda *args: _default_by_steps_weight_fn(*args,
gamma=gamma)
else:
weight_fn = _default_by_episodes_weight_fn
if by_steps:
steps = dataset.get_all_steps(limit=limit)
rewards = reward_fn(steps)
weights = weight_fn(steps)
else:
episodes, valid_steps = dataset.get_all_episodes(
truncate_episode_at=truncate_episode_at, limit=limit)
rewards = reward_fn(episodes, valid_steps)
weights = weight_fn(episodes, valid_steps)
rewards = common_lib.reverse_broadcast(rewards, weights)
weights = common_lib.reverse_broadcast(weights, rewards)
if tf.rank(weights) < 2:
return (tf.reduce_sum(rewards * weights, axis=0) /
tf.reduce_sum(weights, axis=0))
return (tf.linalg.matmul(weights, rewards) /
tf.reduce_sum(tf.math.reduce_mean(weights, axis=0)))
def solve(self,
dataset: dataset_lib.OffpolicyDataset,
target_policy: tf_policy.TFPolicy,
regularizer: float = 1e-8):
"""Solves for density ratios and then approximates target policy value.
Args:
dataset: The dataset to sample experience from.
target_policy: The policy whose value we want to estimate.
regularizer: A small constant to add to matrices before inverting them or
to floats before taking square root.
Returns:
Estimated average per-step reward of the target policy.
"""
td_residuals = np.zeros([self._dimension, self._dimension])
total_weights = np.zeros([self._dimension])
initial_weights = np.zeros([self._dimension])
episodes, valid_steps = dataset.get_all_episodes(limit=None)
tfagents_episodes = dataset_lib.convert_to_tfagents_timestep(episodes)
for episode_num in range(tf.shape(valid_steps)[0]):
# Precompute probabilites for this episode.
this_episode = tf.nest.map_structure(lambda t: t[episode_num],
episodes)
first_step = tf.nest.map_structure(lambda t: t[0], this_episode)
this_tfagents_episode = dataset_lib.convert_to_tfagents_timestep(
this_episode)
episode_target_log_probabilities = target_policy.distribution(
this_tfagents_episode).action.log_prob(this_episode.action)
episode_target_probs = target_policy.distribution(
this_tfagents_episode).action.probs_parameter()
for step_num in range(tf.shape(valid_steps)[1] - 1):
this_step = tf.nest.map_structure(
lambda t: t[episode_num, step_num], episodes)
next_step = tf.nest.map_structure(
lambda t: t[episode_num, step_num + 1], episodes)
if this_step.is_last() or not valid_steps[episode_num,
step_num]:
continue
weight = 1.0
nu_index = self._get_index(this_step.observation,
this_step.action)
td_residuals[nu_index, nu_index] += weight
total_weights[nu_index] += weight
policy_ratio = 1.0
if not self._solve_for_state_action_ratio:
policy_ratio = tf.exp(
episode_target_log_probabilities[step_num] -
this_step.get_log_probability())
# Need to weight next nu by importance weight.
next_weight = (weight if self._solve_for_state_action_ratio
else policy_ratio * weight)
next_probs = episode_target_probs[step_num + 1]
for next_action, next_prob in enumerate(next_probs):
next_nu_index = self._get_index(next_step.observation,
next_action)
td_residuals[next_nu_index,
nu_index] += (-next_prob * self._gamma *
next_weight)
initial_probs = episode_target_probs[0]
for initial_action, initial_prob in enumerate(initial_probs):
initial_nu_index = self._get_index(first_step.observation,
initial_action)
initial_weights[initial_nu_index] += weight * initial_prob
td_residuals /= np.sqrt(regularizer + total_weights)[None, :]
td_errors = np.dot(td_residuals, td_residuals.T)
self._nu = np.linalg.solve(
td_errors + regularizer * np.eye(self._dimension),
(1 - self._gamma) * initial_weights)
self._zeta = np.dot(
self._nu, td_residuals) / np.sqrt(regularizer + total_weights)
return self.estimate_average_reward(dataset, target_policy)
def solve_nu_zeta(self,
dataset: dataset_lib.OffpolicyDataset,
target_policy: tf_policy.TFPolicy,
regularizer: float = 1e-6):
"""Solves for density ratios and then approximates target policy value.
Args:
dataset: The dataset to sample experience from.
target_policy: The policy whose value we want to estimate.
regularizer: A small constant to add to matrices before inverting them or
to floats before taking square root.
Returns:
Estimated average per-step reward of the target policy.
"""
if not hasattr(self, '_td_mat'):
# Set up env_steps.
episodes, valid_steps = dataset.get_all_episodes(
limit=self._limit_episodes)
total_num_steps_per_episode = tf.shape(valid_steps)[1] - 1
num_episodes = tf.shape(valid_steps)[0]
num_samples = num_episodes * total_num_steps_per_episode
valid_and_not_last = tf.logical_and(valid_steps,
episodes.discount > 0)
valid_indices = tf.squeeze(
tf.where(tf.reshape(valid_and_not_last[:, :-1], [-1])))
initial_env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(
tf.repeat(t[:, 0:1, ...],
axis=1,
repeats=total_num_steps_per_episode),
[num_samples, -1])), episodes)
initial_env_step = tf.nest.map_structure(
lambda t: tf.gather(t, valid_indices), initial_env_step)
tfagents_initial_env_step = dataset_lib.convert_to_tfagents_timestep(
initial_env_step)
env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(t[:, 0:total_num_steps_per_episode, ...],
[num_samples, -1])), episodes)
env_step = tf.nest.map_structure(
lambda t: tf.gather(t, valid_indices), env_step)
tfagents_env_step = dataset_lib.convert_to_tfagents_timestep(
env_step)
next_env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(t[:, 1:total_num_steps_per_episode + 1, ...],
[num_samples, -1])), episodes)
next_env_step = tf.nest.map_structure(
lambda t: tf.gather(t, valid_indices), next_env_step)
tfagents_next_env_step = dataset_lib.convert_to_tfagents_timestep(
next_env_step)
# get probabilities
initial_target_probs = target_policy.distribution(
tfagents_initial_env_step).action.probs_parameter()
next_target_probs = target_policy.distribution(
tfagents_next_env_step).action.probs_parameter()
# First, get the nu_loss and data weights
#current_nu_loss = self._get_nu_loss(initial_env_step, env_step,
# next_env_step, target_policy)
#data_weight, _ = self._get_weights(current_nu_loss)
# # debug only and to reproduce dual dice result, DELETE
# data_weight = tf.ones_like(data_weight)
state_action_count = self._get_state_action_counts(env_step)
counts = tf.reduce_sum(
tf.one_hot(state_action_count, self._dimension), 0)
gamma_sample = tf.pow(self._gamma,
tf.cast(env_step.step_num, tf.float32))
# # debug only and to reproduce dual dice result, DELETE
# gamma_sample = tf.ones_like(gamma_sample)
# now we need to expand_dims to include action space in extra dimensions
#data_weights = tf.reshape(data_weight, [-1, self._num_limits])
# both are data sample weights for L2 problem, needs to be normalized later
#gamma_data_weights = tf.reshape(gamma_sample, [-1, 1]) * data_weights
initial_states = tf.tile(
tf.reshape(initial_env_step.observation, [-1, 1]),
[1, self._num_actions])
initial_actions = tf.tile(
tf.reshape(tf.range(self._num_actions), [1, -1]),
[initial_env_step.observation.shape[0], 1])
initial_nu_indices = self._get_index(initial_states,
initial_actions)
# linear term w.r.t. initial distribution
#b_vec_2 = tf.stack([
# tf.reduce_sum(
# tf.reshape(
# data_weights[:, itr] / tf.reduce_sum(data_weights[:, itr]),
# [-1, 1]) * tf.reduce_sum(
# tf.one_hot(initial_nu_indices, self._dimension) *
# (1 - self._gamma) *
# tf.expand_dims(initial_target_probs, axis=-1),
# axis=1),
# axis=0) for itr in range(self._num_limits)
#],
# axis=0)
next_states = tf.tile(
tf.reshape(next_env_step.observation, [-1, 1]),
[1, self._num_actions])
next_actions = tf.tile(
tf.reshape(tf.range(self._num_actions), [1, -1]),
[next_env_step.observation.shape[0], 1])
next_nu_indices = self._get_index(next_states, next_actions)
next_nu_indices = tf.where(
tf.expand_dims(next_env_step.is_absorbing(), -1),
-1 * tf.ones_like(next_nu_indices), next_nu_indices)
nu_indices = self._get_index(env_step.observation, env_step.action)
target_log_probabilities = target_policy.distribution(
tfagents_env_step).action.log_prob(env_step.action)
if not self._solve_for_state_action_ratio:
policy_ratio = tf.exp(target_log_probabilities -
env_step.get_log_probability())
else:
policy_ratio = tf.ones([
target_log_probabilities.shape[0],
])
policy_ratios = tf.tile(tf.reshape(policy_ratio, [-1, 1]),
[1, self._num_actions])
# the tabular feature vector
a_vec = tf.one_hot(nu_indices, self._dimension) - tf.reduce_sum(
self._gamma *
tf.expand_dims(next_target_probs * policy_ratios, axis=-1) *
tf.one_hot(next_nu_indices, self._dimension),
axis=1)
# linear term w.r.t. reward
#b_vec_1 = tf.stack([
# tf.reduce_sum(
# tf.reshape(
# (gamma_data_weights[:, itr] /
# tf.reduce_sum(gamma_data_weights[:, itr])) * self._reward_fn(env_step), #/
# #tf.cast(state_action_count, tf.float32),
# [-1, 1]) * a_vec,
# axis=0) for itr in range(self._num_limits)
#],
# axis=0)
# quadratic term of feature
# Get weighted outer product by using einsum to save computing resource!
#a_mat = tf.stack([
# tf.einsum(
# 'ai, a, aj -> ij', a_vec,
# #1.0 / tf.cast(state_action_count, tf.float32),
# gamma_data_weights[:, itr] /
# tf.reduce_sum(gamma_data_weights[:, itr]),
# a_vec)
# for itr in range(self._num_limits)
#],
# axis=0)
td_mat = tf.einsum('ai, a, aj -> ij',
tf.one_hot(nu_indices, self._dimension),
1.0 / tf.cast(state_action_count, tf.float32),
a_vec)
weighted_rewards = policy_ratio * self._reward_fn(env_step)
bias = tf.reduce_sum(
tf.one_hot(nu_indices, self._dimension) *
tf.reshape(weighted_rewards, [-1, 1]) * 1.0 /
tf.cast(state_action_count, tf.float32)[:, None],
axis=0)
# Initialize
self._nu = np.ones_like(self._nu) * bias[:, None]
self._nu2 = np.ones_like(self._nu2) * bias[:, None]
self._a_vec = a_vec
self._td_mat = td_mat
self._bias = bias
self._weighted_rewards = weighted_rewards
self._state_action_count = state_action_count
self._nu_indices = nu_indices
self._initial_nu_indices = initial_nu_indices
self._initial_target_probs = initial_target_probs
self._gamma_sample = gamma_sample
self._gamma_sample = tf.ones_like(gamma_sample)
saddle_bellman_residuals = (tf.matmul(self._a_vec, self._nu) -
self._weighted_rewards[:, None])
saddle_bellman_residuals *= -1 * self._algae_alpha_sign
saddle_zetas = tf.gather(self._zeta, self._nu_indices)
saddle_initial_nu_values = tf.reduce_sum( # Average over actions.
self._initial_target_probs[:, :, None] *
tf.gather(self._nu, self._initial_nu_indices),
axis=1)
saddle_init_nu_loss = ((1 - self._gamma) * saddle_initial_nu_values *
self._algae_alpha_sign)
saddle_bellman_residuals2 = (tf.matmul(self._a_vec, self._nu2) -
self._weighted_rewards[:, None])
saddle_bellman_residuals2 *= 1 * self._algae_alpha_sign
saddle_zetas2 = tf.gather(self._zeta2, self._nu_indices)
saddle_initial_nu_values2 = tf.reduce_sum( # Average over actions.
self._initial_target_probs[:, :, None] *
tf.gather(self._nu2, self._initial_nu_indices),
axis=1)
saddle_init_nu_loss2 = ((1 - self._gamma) * saddle_initial_nu_values2 *
-1 * self._algae_alpha_sign)
saddle_loss = 0.5 * (
saddle_init_nu_loss + saddle_bellman_residuals * saddle_zetas +
-tf.math.abs(self._algae_alpha) * 0.5 * tf.square(saddle_zetas) +
-saddle_init_nu_loss2 + -saddle_bellman_residuals2 * saddle_zetas2
+ tf.math.abs(self._algae_alpha) * 0.5 * tf.square(saddle_zetas2))
# Binary search to find best alpha.
left = tf.constant([-8., -8.])
right = tf.constant([32., 32.])
for _ in range(16):
mid = 0.5 * (left + right)
self._alpha.assign(mid)
weights, log_weights = self._get_weights(
saddle_loss * self._gamma_sample[:, None])
divergence = self._compute_divergence(weights, log_weights)
divergence_violation = divergence - self._two_sided_limit
left = tf.where(divergence_violation > 0., mid, left)
right = tf.where(divergence_violation > 0., right, mid)
self._alpha.assign(0.5 * (left + right))
weights, log_weights = self._get_weights(saddle_loss *
self._gamma_sample[:, None])
gamma_data_weights = tf.stop_gradient(weights *
self._gamma_sample[:, None])
#print(tf.concat([gamma_data_weights, saddle_loss], axis=-1))
avg_saddle_loss = (
tf.reduce_sum(gamma_data_weights * saddle_loss, axis=0) /
tf.reduce_sum(gamma_data_weights, axis=0))
weighted_state_action_count = tf.reduce_sum(
tf.one_hot(self._nu_indices, self._dimension)[:, :, None] *
weights[:, None, :],
axis=0)
weighted_state_action_count = tf.gather(weighted_state_action_count,
self._nu_indices)
my_td_mat = tf.einsum(
'ai, ab, ab, aj -> bij',
tf.one_hot(self._nu_indices, self._dimension),
#1.0 / tf.cast(self._state_action_count, tf.float32),
1.0 / weighted_state_action_count,
weights,
self._a_vec)
my_bias = tf.reduce_sum(
tf.transpose(weights)[:, :, None] *
tf.one_hot(self._nu_indices, self._dimension)[None, :, :] *
tf.reshape(self._weighted_rewards, [1, -1, 1]) *
#1.0 / tf.cast(self._state_action_count, tf.float32)[None, :, None],
1.0 / tf.transpose(weighted_state_action_count)[:, :, None],
axis=1)
#print('hello', saddle_initial_nu_values[:1], saddle_zetas[:3],
# self._nu[:2], my_bias[:, :2], saddle_loss[:4])
with tf.GradientTape(watch_accessed_variables=False,
persistent=True) as tape:
tape.watch([self._nu, self._nu2, self._alpha])
bellman_residuals = tf.matmul(
my_td_mat,
tf.transpose(self._nu)[:, :, None]) - my_bias[:, :, None]
bellman_residuals = tf.transpose(tf.squeeze(bellman_residuals, -1))
bellman_residuals = tf.gather(bellman_residuals, self._nu_indices)
initial_nu_values = tf.reduce_sum( # Average over actions.
self._initial_target_probs[:, :, None] *
tf.gather(self._nu, self._initial_nu_indices),
axis=1)
bellman_residuals *= self._algae_alpha_sign
init_nu_loss = ((1 - self._gamma) * initial_nu_values *
self._algae_alpha_sign)
nu_loss = (tf.math.square(bellman_residuals) / 2.0 +
tf.math.abs(self._algae_alpha) * init_nu_loss)
loss = (gamma_data_weights * nu_loss /
tf.reduce_sum(gamma_data_weights, axis=0, keepdims=True))
bellman_residuals2 = tf.matmul(
my_td_mat,
tf.transpose(self._nu2)[:, :, None]) - my_bias[:, :, None]
bellman_residuals2 = tf.transpose(
tf.squeeze(bellman_residuals2, -1))
bellman_residuals2 = tf.gather(bellman_residuals2,
self._nu_indices)
initial_nu_values2 = tf.reduce_sum( # Average over actions.
self._initial_target_probs[:, :, None] *
tf.gather(self._nu2, self._initial_nu_indices),
axis=1)
bellman_residuals2 *= -1 * self._algae_alpha_sign
init_nu_loss2 = ((1 - self._gamma) * initial_nu_values2 * -1 *
self._algae_alpha_sign)
nu_loss2 = (tf.math.square(bellman_residuals2) / 2.0 +
tf.math.abs(self._algae_alpha) * init_nu_loss2)
loss2 = (gamma_data_weights * nu_loss2 /
tf.reduce_sum(gamma_data_weights, axis=0, keepdims=True))
divergence = self._compute_divergence(weights, log_weights)
divergence_violation = divergence - self._two_sided_limit
alpha_loss = (-tf.exp(self._alpha) *
tf.stop_gradient(divergence_violation))
extra_loss = tf.reduce_sum(tf.math.square(self._nu[-1, :]))
extra_loss2 = tf.reduce_sum(tf.math.square(self._nu2[-1, :]))
nu_grad = tape.gradient(loss + extra_loss, [self._nu])[0]
nu_grad2 = tape.gradient(loss2 + extra_loss2, [self._nu2])[0]
avg_loss = tf.reduce_sum(0.5 * (loss - loss2) /
tf.math.abs(self._algae_alpha),
axis=0)
nu_jacob = tape.jacobian(nu_grad, [self._nu])[0]
nu_hess = tf.stack(
[nu_jacob[:, i, :, i] for i in range(self._num_limits)], axis=0)
nu_jacob2 = tape.jacobian(nu_grad2, [self._nu2])[0]
nu_hess2 = tf.stack(
[nu_jacob2[:, i, :, i] for i in range(self._num_limits)], axis=0)
for idx, div in enumerate(divergence):
tf.summary.scalar('divergence%d' % idx, div)
#alpha_grads = tape.gradient(alpha_loss, [self._alpha])
#alpha_grad_op = self._alpha_optimizer.apply_gradients(
# zip(alpha_grads, [self._alpha]))
#self._alpha.assign(tf.minimum(8., tf.maximum(-8., self._alpha)))
#print(self._alpha, tf.concat([weights, nu_loss], -1))
#regularizer = 0.1
nu_transformed = tf.transpose(
tf.squeeze(
tf.linalg.solve(
nu_hess + regularizer * tf.eye(self._dimension),
tf.expand_dims(-tf.transpose(nu_grad), axis=-1))))
self._nu = self._nu + 0.1 * nu_transformed
nu_transformed2 = tf.transpose(
tf.squeeze(
tf.linalg.solve(
nu_hess2 + regularizer * tf.eye(self._dimension),
tf.expand_dims(-tf.transpose(nu_grad2), axis=-1))))
self._nu2 = self._nu2 + 0.1 * nu_transformed2
print(avg_loss * self._algae_alpha_sign,
avg_saddle_loss * self._algae_alpha_sign, self._nu[:2],
divergence)
#print(init_nu_loss[:8], init_nu_loss[-8:])
#print(bellman_residuals[:8])
#print(self._nu[:3], self._zeta[:3])
zetas = tf.matmul(my_td_mat,
tf.transpose(self._nu)[:, :, None]) - my_bias[:, :,
None]
zetas = tf.transpose(tf.squeeze(zetas, -1))
zetas *= -self._algae_alpha_sign
zetas /= tf.math.abs(self._algae_alpha)
self._zeta = self._zeta + 0.1 * (zetas - self._zeta)
zetas2 = tf.matmul(my_td_mat,
tf.transpose(self._nu2)[:, :, None]) - my_bias[:, :,
None]
zetas2 = tf.transpose(tf.squeeze(zetas2, -1))
zetas2 *= 1 * self._algae_alpha_sign
zetas2 /= tf.math.abs(self._algae_alpha)
self._zeta2 = self._zeta2 + 0.1 * (zetas2 - self._zeta2)
#self._zeta = (
# tf.einsum('ij,ja-> ia', self._td_mat, self._nu) -
# tf.transpose(my_bias))
#self._zeta *= -tf.reshape(self._algae_alpha_sign, [1, self._num_limits])
#self._zeta /= tf.math.abs(self._algae_alpha)
return [
avg_saddle_loss * self._algae_alpha_sign,
avg_loss * self._algae_alpha_sign, divergence
]
def prepare_dataset(self, dataset: dataset_lib.OffpolicyDataset,
target_policy: tf_policy.TFPolicy):
"""Performs pre-computations on dataset to make solving easier."""
episodes, valid_steps = dataset.get_all_episodes(limit=self._limit_episodes)
total_num_steps_per_episode = tf.shape(valid_steps)[1] - 1
num_episodes = tf.shape(valid_steps)[0]
num_samples = num_episodes * total_num_steps_per_episode
valid_and_not_last = tf.logical_and(valid_steps, episodes.discount > 0)
valid_indices = tf.squeeze(
tf.where(tf.reshape(valid_and_not_last[:, :-1], [-1])))
# Flatten all tensors so that each data sample is a tuple of
# (initial_env_step, env_step, next_env_step).
initial_env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(
tf.repeat(
t[:, 0:1, ...], axis=1, repeats=total_num_steps_per_episode
), [num_samples, -1])), episodes)
initial_env_step = tf.nest.map_structure(
lambda t: tf.gather(t, valid_indices), initial_env_step)
tfagents_initial_env_step = dataset_lib.convert_to_tfagents_timestep(
initial_env_step)
env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(t[:, 0:total_num_steps_per_episode, ...],
[num_samples, -1])), episodes)
env_step = tf.nest.map_structure(lambda t: tf.gather(t, valid_indices),
env_step)
tfagents_env_step = dataset_lib.convert_to_tfagents_timestep(env_step)
next_env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(t[:, 1:total_num_steps_per_episode + 1, ...],
[num_samples, -1])), episodes)
next_env_step = tf.nest.map_structure(lambda t: tf.gather(t, valid_indices),
next_env_step)
tfagents_next_env_step = dataset_lib.convert_to_tfagents_timestep(
next_env_step)
# Get target probabilities for initial and next steps.
initial_target_probs = target_policy.distribution(
tfagents_initial_env_step).action.probs_parameter()
next_target_probs = target_policy.distribution(
tfagents_next_env_step).action.probs_parameter()
# Map states and actions to indices into tabular representation.
initial_states = tf.tile(
tf.reshape(initial_env_step.observation, [-1, 1]),
[1, self._num_actions])
initial_actions = tf.tile(
tf.reshape(tf.range(self._num_actions), [1, -1]),
[initial_env_step.observation.shape[0], 1])
initial_nu_indices = self._get_index(initial_states, initial_actions)
next_states = tf.tile(
tf.reshape(next_env_step.observation, [-1, 1]), [1, self._num_actions])
next_actions = tf.tile(
tf.reshape(tf.range(self._num_actions), [1, -1]),
[next_env_step.observation.shape[0], 1])
next_nu_indices = self._get_index(next_states, next_actions)
next_nu_indices = tf.where(
tf.expand_dims(next_env_step.is_absorbing(), -1),
-1 * tf.ones_like(next_nu_indices), next_nu_indices)
nu_indices = self._get_index(env_step.observation, env_step.action)
target_log_probabilities = target_policy.distribution(
tfagents_env_step).action.log_prob(env_step.action)
if not self._solve_for_state_action_ratio:
policy_ratio = tf.exp(target_log_probabilities -
env_step.get_log_probability())
else:
policy_ratio = tf.ones([
target_log_probabilities.shape[0],
])
policy_ratios = tf.tile(
tf.reshape(policy_ratio, [-1, 1]), [1, self._num_actions])
# Bellman residual matrix of size [n_data, n_dim].
a_vec = tf.one_hot(nu_indices, self._dimension) - tf.reduce_sum(
self._gamma *
tf.expand_dims(next_target_probs * policy_ratios, axis=-1) *
tf.one_hot(next_nu_indices, self._dimension),
axis=1)
state_action_count = self._get_state_action_counts(env_step)
# Bellman residual matrix of size [n_dim, n_dim].
td_mat = tf.einsum('ai, a, aj -> ij', tf.one_hot(nu_indices,
self._dimension),
1.0 / tf.cast(state_action_count, tf.float32), a_vec)
# Reward vector of size [n_data].
weighted_rewards = policy_ratio * self._reward_fn(env_step)
# Reward vector of size [n_dim].
bias = tf.reduce_sum(
tf.one_hot(nu_indices, self._dimension) *
tf.reshape(weighted_rewards, [-1, 1]) * 1.0 /
tf.cast(state_action_count, tf.float32)[:, None],
axis=0)
# Initialize.
self._nu = np.ones_like(self._nu) * bias[:, None]
self._nu2 = np.ones_like(self._nu2) * bias[:, None]
self._a_vec = a_vec
self._td_mat = td_mat
self._bias = bias
self._weighted_rewards = weighted_rewards
self._state_action_count = state_action_count
self._nu_indices = nu_indices
self._initial_nu_indices = initial_nu_indices
self._initial_target_probs = initial_target_probs
def solve(self,
dataset: dataset_lib.OffpolicyDataset,
target_policy: tf_policy.TFPolicy,
regularizer: float = 1e-8):
"""Solves for Q-values and then approximates target policy value.
Args:
dataset: The dataset to sample experience from.
target_policy: The policy whose value we want to estimate.
regularizer: A small constant to add before dividing.
Returns:
Estimated average per-step reward of the target policy.
"""
num_estimates = 1 + int(self._num_qvalues)
transition_matrix = np.zeros(
[self._dimension, self._dimension, num_estimates])
reward_vector = np.zeros(
[self._dimension, num_estimates, self._num_perturbations])
total_weights = np.zeros([self._dimension, num_estimates])
episodes, valid_steps = dataset.get_all_episodes(limit=self._limit_episodes)
#all_rewards = self._reward_fn(episodes)
#reward_std = np.ma.MaskedArray(all_rewards, valid_steps).std()
tfagents_episodes = dataset_lib.convert_to_tfagents_timestep(episodes)
sample_weights = np.array(valid_steps, dtype=np.int64)
if not self._bootstrap or self._num_qvalues is None:
sample_weights = (
sample_weights[:, :, None] * np.ones([1, 1, num_estimates]))
else:
probs = np.reshape(sample_weights, [-1]) / np.sum(sample_weights)
weights = np.random.multinomial(
np.sum(sample_weights), probs,
size=self._num_qvalues).astype(np.float32)
weights = np.reshape(
np.transpose(weights),
list(np.shape(sample_weights)) + [self._num_qvalues])
sample_weights = np.concatenate([sample_weights[:, :, None], weights],
axis=-1)
for episode_num in range(tf.shape(valid_steps)[0]):
# Precompute probabilites for this episode.
this_episode = tf.nest.map_structure(lambda t: t[episode_num], episodes)
this_tfagents_episode = dataset_lib.convert_to_tfagents_timestep(
this_episode)
episode_target_log_probabilities = target_policy.distribution(
this_tfagents_episode).action.log_prob(this_episode.action)
episode_target_probs = target_policy.distribution(
this_tfagents_episode).action.probs_parameter()
for step_num in range(tf.shape(valid_steps)[1] - 1):
this_step = tf.nest.map_structure(lambda t: t[episode_num, step_num],
episodes)
next_step = tf.nest.map_structure(
lambda t: t[episode_num, step_num + 1], episodes)
this_tfagents_step = dataset_lib.convert_to_tfagents_timestep(this_step)
next_tfagents_step = dataset_lib.convert_to_tfagents_timestep(next_step)
this_weights = sample_weights[episode_num, step_num, :]
if this_step.is_last() or not valid_steps[episode_num, step_num]:
continue
weight = this_weights
this_index = self._get_index(this_step.observation, this_step.action)
reward_vector[this_index, :, :] += np.expand_dims(
self._reward_fn(this_step) * weight, -1)
if self._num_qvalues is not None:
random_noise = np.random.binomial(this_weights[1:].astype('int64'),
0.5)
reward_vector[this_index, 1:, :] += (
self._perturbation_scale[None, :] *
(2 * random_noise - this_weights[1:])[:, None])
total_weights[this_index] += weight
policy_ratio = 1.0
if not self._solve_for_state_action_value:
policy_ratio = tf.exp(episode_target_log_probabilities[step_num] -
this_step.get_log_probability())
# Need to weight next nu by importance weight.
next_weight = (
weight if self._solve_for_state_action_value else policy_ratio *
weight)
if next_step.is_absorbing():
next_index = -1 # Absorbing state.
transition_matrix[this_index, next_index] += next_weight
else:
next_probs = episode_target_probs[step_num + 1]
for next_action, next_prob in enumerate(next_probs):
next_index = self._get_index(next_step.observation, next_action)
transition_matrix[this_index, next_index] += next_prob * next_weight
print('Done processing data.')
transition_matrix /= (regularizer + total_weights)[:, None, :]
reward_vector /= (regularizer + total_weights)[:, :, None]
reward_vector[np.where(np.equal(total_weights,
0.0))] = self._default_reward_value
reward_vector[-1, :, :] = 0.0 # Terminal absorbing state has 0 reward.
self._point_qvalues = np.linalg.solve(
np.eye(self._dimension) - self._gamma * transition_matrix[:, :, 0],
reward_vector[:, 0])
if self._num_qvalues is not None:
self._ensemble_qvalues = np.linalg.solve(
(np.eye(self._dimension) -
self._gamma * np.transpose(transition_matrix, [2, 0, 1])),
np.transpose(reward_vector, [1, 0, 2]))
return self.estimate_average_reward(dataset, target_policy)
def prepare_dataset(self, dataset: dataset_lib.OffpolicyDataset,
target_policy: tf_policy.TFPolicy):
episodes, valid_steps = dataset.get_all_episodes()
tfagents_episodes = dataset_lib.convert_to_tfagents_timestep(episodes)
for episode_num in range(tf.shape(valid_steps)[0]):
# Precompute probabilites for this episode.
this_episode = tf.nest.map_structure(lambda t: t[episode_num],
episodes)
first_step = tf.nest.map_structure(lambda t: t[0], this_episode)
this_tfagents_episode = dataset_lib.convert_to_tfagents_timestep(
this_episode)
episode_target_log_probabilities = target_policy.distribution(
this_tfagents_episode).action.log_prob(this_episode.action)
episode_target_probs = target_policy.distribution(
this_tfagents_episode).action.probs_parameter()
for step_num in range(tf.shape(valid_steps)[1] - 1):
this_step = tf.nest.map_structure(
lambda t: t[episode_num, step_num], episodes)
next_step = tf.nest.map_structure(
lambda t: t[episode_num, step_num + 1], episodes)
if this_step.is_last() or not valid_steps[episode_num,
step_num]:
continue
weight = 1.0
nu_index = self._get_index(this_step.observation,
this_step.action)
self._td_residuals[nu_index, nu_index] += -weight
self._total_weights[nu_index] += weight
policy_ratio = 1.0
if not self._solve_for_state_action_ratio:
policy_ratio = tf.exp(
episode_target_log_probabilities[step_num] -
this_step.get_log_probability())
# Need to weight next nu by importance weight.
next_weight = (weight if self._solve_for_state_action_ratio
else policy_ratio * weight)
next_probs = episode_target_probs[step_num + 1]
for next_action, next_prob in enumerate(next_probs):
next_nu_index = self._get_index(next_step.observation,
next_action)
self._td_residuals[next_nu_index,
nu_index] += (next_prob * self._gamma *
next_weight)
initial_probs = episode_target_probs[0]
for initial_action, initial_prob in enumerate(initial_probs):
initial_nu_index = self._get_index(first_step.observation,
initial_action)
self._initial_weights[
initial_nu_index] += weight * initial_prob
self._initial_weights = tf.cast(self._initial_weights, tf.float32)
self._total_weights = tf.cast(self._total_weights, tf.float32)
self._td_residuals = self._td_residuals / np.sqrt(
1e-8 + self._total_weights)[None, :]
self._td_errors = tf.cast(
np.dot(self._td_residuals, self._td_residuals.T), tf.float32)
self._td_residuals = tf.cast(self._td_residuals, tf.float32)
def estimate_reward_ci(self,
dataset: dataset_lib.OffpolicyDataset,
target_policy: tf_policy.TFPolicy,
episode_limit: Optional[int] = None,
num_grid: Optional[int] = 100,
eps: Optional[float] = 1e-6,
num_bootstraps: Optional[int] = 10000,
num_bootstrap_samples: Optional[int] = 10000):
"""Estimate the confidence interval of reward."""
is_weighted_reward_samples = self.get_is_weighted_reward_samples(
dataset, target_policy, episode_limit)
episodes, valid_steps = dataset.get_all_episodes(limit=episode_limit)
num_episodes = tf.shape(valid_steps)[0]
max_abs_reward = tf.reduce_max(
tf.where(valid_steps, tf.abs(self._reward_fn(episodes)), 0.))
# mean estimate
center = self.estimate_average_reward(dataset, target_policy)
delta_tail_half = self._delta_tail / 2.0
num_episodes_float = tf.cast(num_episodes, tf.float32)
if self._ci_method == 'CH': # Chernoff-Hoeffding
width = max_abs_reward * tf.math.sqrt(
tf.math.log(1.0 / delta_tail_half) / num_episodes_float)
lb = center - width
ub = center + width
elif self._ci_method == 'BE': # Empirical Bernstein
constant_term = 7 * max_abs_reward * tf.math.log(
2.0 / delta_tail_half) / (3 * (num_episodes_float - 1))
is_weighted_reward_samples_2d = tf.reshape(
is_weighted_reward_samples, [-1, 1])
variance_term = tf.reduce_sum(
tf.square(
tf.tile(is_weighted_reward_samples_2d, [1, num_episodes]) -
is_weighted_reward_samples_2d))
variance_term *= tf.math.log(
2.0 / delta_tail_half) / (num_episodes_float - 1)
width = constant_term + tf.math.sqrt(
variance_term) / num_episodes_float
lb = center - width
ub = center + width
elif self._ci_method == 'C-BE': # Clipped empirical Bernstein
# need to learn c
def compute_center_width(c_const):
"""Compute the center and width of CI."""
c_vec = c_const * tf.ones_like(is_weighted_reward_samples)
c_is_weighted_reward_samples = tf.minimum(
is_weighted_reward_samples, c_vec) / c_vec
c_is_weighted_reward_samples_2d = tf.reshape(
c_is_weighted_reward_samples, [-1, 1])
constant_term = 7 * num_episodes_float * tf.math.log(
2.0 / delta_tail_half) / (3 * (num_episodes_float - 1))
variance_term = tf.reduce_sum(
tf.square(
tf.tile(c_is_weighted_reward_samples_2d,
[1, num_episodes]) -
c_is_weighted_reward_samples_2d))
variance_term *= tf.math.log(
2.0 / delta_tail_half) / (num_episodes_float - 1)
width = (constant_term + tf.math.sqrt(variance_term)
) / tf.reduce_sum(1.0 / c_vec)
center = tf.reduce_sum(
c_is_weighted_reward_samples) / tf.reduce_sum(1.0 / c_vec)
return center, width
def compute_bdd(c_const):
center, width = compute_center_width(c_const)
return center - width, center + width
def compute_obj(c_const, obj='width'):
center, width = compute_center_width(c_const)
if obj == 'lb':
return center - width
elif obj == 'ub': # minimize ub
return -(center + width)
elif obj == 'width':
return width
elif obj == 'lb_ub':
return -2 * width
else:
ValueError('Objective is not implemented')
c_grid = tf.linspace(eps, max_abs_reward, num_grid)
objs = tf.map_fn(compute_obj, c_grid, dtype=tf.float32)
star_index = tf.argmax(objs)
c_star = tf.gather(c_grid, star_index)
lb, ub = compute_bdd(c_star)
elif self._ci_method == 'TT': # Student-t test
# Two-tailed confidence intervals
t_statistic_quantile = stats.t.ppf(1 - delta_tail_half,
num_episodes_float - 1)
std_term = tf.math.sqrt(
tf.reduce_sum(tf.square(is_weighted_reward_samples - center)) /
(num_episodes_float - 1))
width = t_statistic_quantile * std_term / tf.math.sqrt(
num_episodes_float)
lb = center - width
ub = center + width
elif self._ci_method == 'BCa': # Bootstrap
# see references
# https://faculty.washington.edu/heagerty/Courses/b572/public/GregImholte-1.pdf
# http://users.stat.umn.edu/~helwig/notes/bootci-Notes.pdf
gaussian_rv = tfp.distributions.Normal(loc=0, scale=1)
def _compute_bootstrap_lb_ub(reward_samples):
"""Compute Efron's bootstrap lb."""
sample_mean = tf.reduce_mean(reward_samples)
# Step 1, sample with replacement and compute subsampled mean
uniform_log_prob = tf.tile(
tf.expand_dims(tf.zeros(num_episodes), 0),
[num_bootstraps, 1])
ind = tf.random.categorical(uniform_log_prob,
num_bootstrap_samples)
bootstrap_subsamples = tf.gather(reward_samples, ind)
subsample_means = tf.reduce_mean(bootstrap_subsamples, axis=1)
# Step 2, sort subsample means, compute y, z_0, and a
sorted_subsample_means = tf.sort(subsample_means,
axis=0,
direction='ASCENDING')
# bias factor
z_0 = gaussian_rv.quantile(
tf.reduce_sum(
tf.cast(
tf.greater(sample_mean, sorted_subsample_means),
tf.float32)) / float(num_bootstraps))
# y is the leave-one-out, jackknife sample mean
mask_matrix = tf.ones([num_episodes, num_episodes
]) - tf.eye(num_episodes)
leave_one_out_subsample_sums = tf.einsum(
'j,jk->k', reward_samples, mask_matrix)
ys = leave_one_out_subsample_sums / (num_episodes_float - 1)
# average of jackknife estimate
y_bar = tf.reduce_mean(ys)
# acceleration factor
d_ys = y_bar - ys
a = tf.reduce_sum(tf.pow(d_ys, 3.0)) / tf.maximum(
eps, 6.0 * tf.pow(tf.reduce_sum(tf.pow(d_ys, 2.0)), 1.5))
# Step 3, compute z_scores for lb and ub
z_score_delta_tail = gaussian_rv.quantile(delta_tail_half)
z_score_1_delta_tail = gaussian_rv.quantile(1.0 -
delta_tail_half)
z_lb = z_0 + (z_score_delta_tail + z_0) / tf.maximum(
eps, 1 - a * (z_score_delta_tail + z_0))
z_ub = z_0 + (z_score_1_delta_tail + z_0) / tf.maximum(
eps, 1 - a * (z_score_1_delta_tail + z_0))
# Step 4, compute corresponding quantiles and get bootstrap intervals
lb_index = tf.cast(
tf.maximum(
tf.minimum(
tf.floor(num_bootstraps * gaussian_rv.cdf(z_lb)),
num_bootstraps - 1), 1), tf.int64)
ub_index = tf.cast(
tf.maximum(
tf.minimum(
tf.floor(num_bootstraps * gaussian_rv.cdf(z_ub)),
num_bootstraps - 1), 1), tf.int64)
lb = tf.gather(sorted_subsample_means, lb_index)
ub = tf.gather(sorted_subsample_means, ub_index)
return lb, ub
lb, ub = _compute_bootstrap_lb_ub(is_weighted_reward_samples)
else:
ValueError('Confidence interval is not implemented!')
return [lb, ub]
def get_is_weighted_reward_samples(self,
dataset: dataset_lib.OffpolicyDataset,
target_policy: tf_policy.TFPolicy,
episode_limit: Optional[int] = None,
eps: Optional[float] = 1e-8):
"""Get the IS weighted reweard samples."""
episodes, valid_steps = dataset.get_all_episodes(limit=episode_limit)
total_num_steps_per_episode = tf.shape(valid_steps)[1] - 1
num_episodes = tf.shape(valid_steps)[0]
num_samples = num_episodes * total_num_steps_per_episode
init_env_step = tf.nest.map_structure(lambda t: t[:, 0, ...], episodes)
env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(t[:, 0:total_num_steps_per_episode, ...],
[num_samples, -1])), episodes)
next_env_step = tf.nest.map_structure(
lambda t: tf.squeeze(
tf.reshape(t[:, 1:1 + total_num_steps_per_episode, ...],
[num_samples, -1])), episodes)
tfagents_env_step = dataset_lib.convert_to_tfagents_timestep(env_step)
gamma_weights = tf.reshape(
tf.pow(self._gamma, tf.cast(env_step.step_num, tf.float32)),
[num_episodes, total_num_steps_per_episode])
rewards = (-self._get_q_value(env_step) + self._reward_fn(env_step) +
self._gamma * next_env_step.discount *
self._get_v_value(next_env_step, target_policy))
rewards = tf.reshape(rewards,
[num_episodes, total_num_steps_per_episode])
init_values = self._get_v_value(init_env_step, target_policy)
init_offset = (1 - self._gamma) * init_values
target_log_probabilities = target_policy.distribution(
tfagents_env_step).action.log_prob(env_step.action)
if tf.rank(target_log_probabilities) > 1:
target_log_probabilities = tf.reduce_sum(target_log_probabilities,
-1)
if self._policy_network is not None:
baseline_policy_log_probability = self._get_log_prob(
self._policy_network, env_step)
if tf.rank(baseline_policy_log_probability) > 1:
baseline_policy_log_probability = tf.reduce_sum(
baseline_policy_log_probability, -1)
policy_log_ratios = tf.reshape(
tf.maximum(
-1.0 / eps, target_log_probabilities -
baseline_policy_log_probability),
[num_episodes, total_num_steps_per_episode])
else:
policy_log_ratios = tf.reshape(
tf.maximum(
-1.0 / eps,
target_log_probabilities - env_step.get_log_probability()),
[num_episodes, total_num_steps_per_episode])
valid_steps_in = valid_steps[:, 0:total_num_steps_per_episode]
mask = tf.cast(
tf.logical_and(valid_steps_in, episodes.discount[:, :-1] > 0.),
tf.float32)
masked_rewards = tf.where(mask > 0, rewards, tf.zeros_like(rewards))
clipped_policy_log_ratios = mask * self.clip_log_factor(
policy_log_ratios)
if self._mode in ['trajectory-wise', 'weighted-trajectory-wise']:
trajectory_avg_rewards = tf.reduce_sum(
masked_rewards * gamma_weights, axis=1) / tf.reduce_sum(
gamma_weights, axis=1)
trajectory_log_ratios = tf.reduce_sum(clipped_policy_log_ratios,
axis=1)
if self._mode == 'trajectory-wise':
trajectory_avg_rewards *= tf.exp(trajectory_log_ratios)
return init_offset + trajectory_avg_rewards
else:
offset = tf.reduce_max(trajectory_log_ratios)
normalized_clipped_ratios = tf.exp(trajectory_log_ratios -
offset)
normalized_clipped_ratios /= tf.maximum(
eps, tf.reduce_mean(normalized_clipped_ratios))
trajectory_avg_rewards *= normalized_clipped_ratios
return init_offset + trajectory_avg_rewards
elif self._mode in ['step-wise', 'weighted-step-wise']:
trajectory_log_ratios = mask * tf.cumsum(policy_log_ratios, axis=1)
if self._mode == 'step-wise':
trajectory_avg_rewards = tf.reduce_sum(
masked_rewards * gamma_weights *
tf.exp(trajectory_log_ratios),
axis=1) / tf.reduce_sum(gamma_weights, axis=1)
return init_offset + trajectory_avg_rewards
else:
# Average over data, for each time step.
offset = tf.reduce_max(trajectory_log_ratios,
axis=0) # TODO: Handle mask.
normalized_imp_weights = tf.exp(trajectory_log_ratios - offset)
normalized_imp_weights /= tf.maximum(
eps,
tf.reduce_sum(mask * normalized_imp_weights, axis=0) /
tf.maximum(eps, tf.reduce_sum(mask, axis=0)))[None, :]
trajectory_avg_rewards = tf.reduce_sum(
masked_rewards * gamma_weights * normalized_imp_weights,
axis=1) / tf.reduce_sum(gamma_weights, axis=1)
return init_offset + trajectory_avg_rewards
else:
ValueError('Estimator is not implemented!')