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# Copyright 2018 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Functions to compute V-trace off-policy actor critic targets.
For details and theory see:
"IMPALA: Scalable Distributed Deep-RL with
Importance Weighted Actor-Learner Architectures"
by Espeholt, Soyer, Munos et al.
See https://arxiv.org/abs/1802.01561 for the full paper.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import collections
import tensorflow as tf
nest = tf.contrib.framework.nest
VTraceFromLogitsReturns = collections.namedtuple(
'VTraceFromLogitsReturns',
['vs', 'pg_advantages', 'log_rhos',
'behaviour_action_log_probs', 'target_action_log_probs'])
VTraceReturns = collections.namedtuple('VTraceReturns', 'vs pg_advantages')
def log_probs_from_logits_and_actions(policy_logits, actions):
"""Computes action log-probs from policy logits and actions.
In the notation used throughout documentation and comments, T refers to the
time dimension ranging from 0 to T-1. B refers to the batch size and
NUM_ACTIONS refers to the number of actions.
Args:
policy_logits: A float32 tensor of shape [T, B, NUM_ACTIONS] with
un-normalized log-probabilities parameterizing a softmax policy.
actions: An int32 tensor of shape [T, B] with actions.
Returns:
A float32 tensor of shape [T, B] corresponding to the sampling log
probability of the chosen action w.r.t. the policy.
"""
policy_logits = tf.convert_to_tensor(policy_logits, dtype=tf.float32)
actions = tf.convert_to_tensor(actions, dtype=tf.int32)
policy_logits.shape.assert_has_rank(3)
actions.shape.assert_has_rank(2)
return -tf.nn.sparse_softmax_cross_entropy_with_logits(
logits=policy_logits, labels=actions)
def from_logits(
behaviour_policy_logits, target_policy_logits, actions,
discounts, rewards, values, bootstrap_value,
clip_rho_threshold=1.0, clip_pg_rho_threshold=1.0,
name='vtrace_from_logits'):
r"""V-trace for softmax policies.
Calculates V-trace actor critic targets for softmax polices as described in
"IMPALA: Scalable Distributed Deep-RL with
Importance Weighted Actor-Learner Architectures"
by Espeholt, Soyer, Munos et al.
Target policy refers to the policy we are interested in improving and
behaviour policy refers to the policy that generated the given
rewards and actions.
In the notation used throughout documentation and comments, T refers to the
time dimension ranging from 0 to T-1. B refers to the batch size and
NUM_ACTIONS refers to the number of actions.
Args:
behaviour_policy_logits: A float32 tensor of shape [T, B, NUM_ACTIONS] with
un-normalized log-probabilities parametrizing the softmax behaviour
policy.
target_policy_logits: A float32 tensor of shape [T, B, NUM_ACTIONS] with
un-normalized log-probabilities parametrizing the softmax target policy.
actions: An int32 tensor of shape [T, B] of actions sampled from the
behaviour policy.
discounts: A float32 tensor of shape [T, B] with the discount encountered
when following the behaviour policy.
rewards: A float32 tensor of shape [T, B] with the rewards generated by
following the behaviour policy.
values: A float32 tensor of shape [T, B] with the value function estimates
wrt. the target policy.
bootstrap_value: A float32 of shape [B] with the value function estimate at
time T.
clip_rho_threshold: A scalar float32 tensor with the clipping threshold for
importance weights (rho) when calculating the baseline targets (vs).
rho^bar in the paper.
clip_pg_rho_threshold: A scalar float32 tensor with the clipping threshold
on rho_s in \rho_s \delta log \pi(a|x) (r + \gamma v_{s+1} - V(x_s)).
name: The name scope that all V-trace operations will be created in.
Returns:
A `VTraceFromLogitsReturns` namedtuple with the following fields:
vs: A float32 tensor of shape [T, B]. Can be used as target to train a
baseline (V(x_t) - vs_t)^2.
pg_advantages: A float 32 tensor of shape [T, B]. Can be used as an
estimate of the advantage in the calculation of policy gradients.
log_rhos: A float32 tensor of shape [T, B] containing the log importance
sampling weights (log rhos).
behaviour_action_log_probs: A float32 tensor of shape [T, B] containing
behaviour policy action log probabilities (log \mu(a_t)).
target_action_log_probs: A float32 tensor of shape [T, B] containing
target policy action probabilities (log \pi(a_t)).
"""
behaviour_policy_logits = tf.convert_to_tensor(
behaviour_policy_logits, dtype=tf.float32)
target_policy_logits = tf.convert_to_tensor(
target_policy_logits, dtype=tf.float32)
actions = tf.convert_to_tensor(actions, dtype=tf.int32)
# Make sure tensor ranks are as expected.
# The rest will be checked by from_action_log_probs.
behaviour_policy_logits.shape.assert_has_rank(3)
target_policy_logits.shape.assert_has_rank(3)
actions.shape.assert_has_rank(2)
with tf.name_scope(name, values=[
behaviour_policy_logits, target_policy_logits, actions,
discounts, rewards, values, bootstrap_value]):
target_action_log_probs = log_probs_from_logits_and_actions(
target_policy_logits, actions)
behaviour_action_log_probs = log_probs_from_logits_and_actions(
behaviour_policy_logits, actions)
log_rhos = target_action_log_probs - behaviour_action_log_probs
vtrace_returns = from_importance_weights(
log_rhos=log_rhos,
discounts=discounts,
rewards=rewards,
values=values,
bootstrap_value=bootstrap_value,
clip_rho_threshold=clip_rho_threshold,
clip_pg_rho_threshold=clip_pg_rho_threshold)
return VTraceFromLogitsReturns(
log_rhos=log_rhos,
behaviour_action_log_probs=behaviour_action_log_probs,
target_action_log_probs=target_action_log_probs,
**vtrace_returns._asdict()
)
def from_importance_weights(
log_rhos, discounts, rewards, values, bootstrap_value,
clip_rho_threshold=1.0, clip_pg_rho_threshold=1.0,
name='vtrace_from_importance_weights'):
r"""V-trace from log importance weights.
Calculates V-trace actor critic targets as described in
"IMPALA: Scalable Distributed Deep-RL with
Importance Weighted Actor-Learner Architectures"
by Espeholt, Soyer, Munos et al.
In the notation used throughout documentation and comments, T refers to the
time dimension ranging from 0 to T-1. B refers to the batch size and
NUM_ACTIONS refers to the number of actions. This code also supports the
case where all tensors have the same number of additional dimensions, e.g.,
`rewards` is [T, B, C], `values` is [T, B, C], `bootstrap_value` is [B, C].
Args:
log_rhos: A float32 tensor of shape [T, B, NUM_ACTIONS] representing the log
importance sampling weights, i.e.
log(target_policy(a) / behaviour_policy(a)). V-trace performs operations
on rhos in log-space for numerical stability.
discounts: A float32 tensor of shape [T, B] with discounts encountered when
following the behaviour policy.
rewards: A float32 tensor of shape [T, B] containing rewards generated by
following the behaviour policy.
values: A float32 tensor of shape [T, B] with the value function estimates
wrt. the target policy.
bootstrap_value: A float32 of shape [B] with the value function estimate at
time T.
clip_rho_threshold: A scalar float32 tensor with the clipping threshold for
importance weights (rho) when calculating the baseline targets (vs).
rho^bar in the paper. If None, no clipping is applied.
clip_pg_rho_threshold: A scalar float32 tensor with the clipping threshold
on rho_s in \rho_s \delta log \pi(a|x) (r + \gamma v_{s+1} - V(x_s)). If
None, no clipping is applied.
name: The name scope that all V-trace operations will be created in.
Returns:
A VTraceReturns namedtuple (vs, pg_advantages) where:
vs: A float32 tensor of shape [T, B]. Can be used as target to
train a baseline (V(x_t) - vs_t)^2.
pg_advantages: A float32 tensor of shape [T, B]. Can be used as the
advantage in the calculation of policy gradients.
"""
log_rhos = tf.convert_to_tensor(log_rhos, dtype=tf.float32)
discounts = tf.convert_to_tensor(discounts, dtype=tf.float32)
rewards = tf.convert_to_tensor(rewards, dtype=tf.float32)
values = tf.convert_to_tensor(values, dtype=tf.float32)
bootstrap_value = tf.convert_to_tensor(bootstrap_value, dtype=tf.float32)
if clip_rho_threshold is not None:
clip_rho_threshold = tf.convert_to_tensor(clip_rho_threshold,
dtype=tf.float32)
if clip_pg_rho_threshold is not None:
clip_pg_rho_threshold = tf.convert_to_tensor(clip_pg_rho_threshold,
dtype=tf.float32)
# Make sure tensor ranks are consistent.
rho_rank = log_rhos.shape.ndims # Usually 2.
values.shape.assert_has_rank(rho_rank)
bootstrap_value.shape.assert_has_rank(rho_rank - 1)
discounts.shape.assert_has_rank(rho_rank)
rewards.shape.assert_has_rank(rho_rank)
if clip_rho_threshold is not None:
clip_rho_threshold.shape.assert_has_rank(0)
if clip_pg_rho_threshold is not None:
clip_pg_rho_threshold.shape.assert_has_rank(0)
with tf.name_scope(name, values=[
log_rhos, discounts, rewards, values, bootstrap_value]):
rhos = tf.exp(log_rhos)
if clip_rho_threshold is not None:
clipped_rhos = tf.minimum(clip_rho_threshold, rhos, name='clipped_rhos')
else:
clipped_rhos = rhos
cs = tf.minimum(1.0, rhos, name='cs')
# Append bootstrapped value to get [v1, ..., v_t+1]
values_t_plus_1 = tf.concat(
[values[1:], tf.expand_dims(bootstrap_value, 0)], axis=0)
deltas = clipped_rhos * (rewards + discounts * values_t_plus_1 - values)
# Note that all sequences are reversed, computation starts from the back.
sequences = (
tf.reverse(discounts, axis=[0]),
tf.reverse(cs, axis=[0]),
tf.reverse(deltas, axis=[0]),
)
# V-trace vs are calculated through a scan from the back to the beginning
# of the given trajectory.
def scanfunc(acc, sequence_item):
discount_t, c_t, delta_t = sequence_item
return delta_t + discount_t * c_t * acc
initial_values = tf.zeros_like(bootstrap_value)
vs_minus_v_xs = tf.scan(
fn=scanfunc,
elems=sequences,
initializer=initial_values,
parallel_iterations=1,
back_prop=False,
name='scan')
# Reverse the results back to original order.
vs_minus_v_xs = tf.reverse(vs_minus_v_xs, [0], name='vs_minus_v_xs')
# Add V(x_s) to get v_s.
vs = tf.add(vs_minus_v_xs, values, name='vs')
# Advantage for policy gradient.
vs_t_plus_1 = tf.concat([
vs[1:], tf.expand_dims(bootstrap_value, 0)], axis=0)
if clip_pg_rho_threshold is not None:
clipped_pg_rhos = tf.minimum(clip_pg_rho_threshold, rhos,
name='clipped_pg_rhos')
else:
clipped_pg_rhos = rhos
pg_advantages = (
clipped_pg_rhos * (rewards + discounts * vs_t_plus_1 - values))
# Make sure no gradients backpropagated through the returned values.
return VTraceReturns(vs=tf.stop_gradient(vs),
pg_advantages=tf.stop_gradient(pg_advantages))