text: # 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.
  
  In addition to the original paper's code, changes have been made
  to support MultiDiscrete action spaces. behaviour_policy_logits,
  target_policy_logits and actions parameters in the entry point
  multi_from_logits method accepts lists of tensors instead of just
  tensors.
  """
  
  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):
      return multi_log_probs_from_logits_and_actions([policy_logits],
                                                     [actions])[0]
  
  
  def multi_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
    ACTION_SPACE refers to the list of numbers each representing a number of
    actions.
  
    Args:
      policy_logits: A list with length of ACTION_SPACE of float32
        tensors of shapes
        [T, B, ACTION_SPACE[0]],
        ...,
        [T, B, ACTION_SPACE[-1]]
        with un-normalized log-probabilities parameterizing a softmax policy.
      actions: A list with length of ACTION_SPACE of int32
        tensors of shapes
        [T, B],
        ...,
        [T, B]
        with actions.
  
    Returns:
      A list with length of ACTION_SPACE of float32
        tensors of shapes
        [T, B],
        ...,
        [T, B]
        corresponding to the sampling log probability
        of the chosen action w.r.t. the policy.
    """
  
      log_probs = []
      for i in range(len(policy_logits)):
          log_probs.append(-tf.nn.sparse_softmax_cross_entropy_with_logits(
              logits=policy_logits[i], labels=actions[i]))
  
      return log_probs
  
  
  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'):
      """multi_from_logits wrapper used only for tests"""
  
      res = multi_from_logits(
          [behaviour_policy_logits], [target_policy_logits], [actions],
          discounts,
          rewards,
          values,
          bootstrap_value,
          clip_rho_threshold=clip_rho_threshold,
          clip_pg_rho_threshold=clip_pg_rho_threshold,
          name=name)
  
      return VTraceFromLogitsReturns(
          vs=res.vs,
          pg_advantages=res.pg_advantages,
          log_rhos=res.log_rhos,
          behaviour_action_log_probs=tf.squeeze(
              res.behaviour_action_log_probs, axis=0),
          target_action_log_probs=tf.squeeze(
              res.target_action_log_probs, axis=0),
      )
  
  
  def multi_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
    ACTION_SPACE refers to the list of numbers each representing a number of
    actions.
  
    Args:
      behaviour_policy_logits: A list with length of ACTION_SPACE of float32
        tensors of shapes
        [T, B, ACTION_SPACE[0]],
        ...,
        [T, B, ACTION_SPACE[-1]]
        with un-normalized log-probabilities parameterizing the softmax behaviour
        policy.
      target_policy_logits: A list with length of ACTION_SPACE of float32
        tensors of shapes
        [T, B, ACTION_SPACE[0]],
        ...,
        [T, B, ACTION_SPACE[-1]]
        with un-normalized log-probabilities parameterizing the softmax target
        policy.
      actions: A list with length of ACTION_SPACE of int32
        tensors of shapes
        [T, B],
        ...,
        [T, B]
        with 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)).
    """
  
      for i in range(len(behaviour_policy_logits)):
          behaviour_policy_logits[i] = tf.convert_to_tensor(
              behaviour_policy_logits[i], dtype=tf.float32)
          target_policy_logits[i] = tf.convert_to_tensor(
              target_policy_logits[i], dtype=tf.float32)
          actions[i] = tf.convert_to_tensor(actions[i], dtype=tf.int32)
  
          # Make sure tensor ranks are as expected.
          # The rest will be checked by from_action_log_probs.
          behaviour_policy_logits[i].shape.assert_has_rank(3)
          target_policy_logits[i].shape.assert_has_rank(3)
          actions[i].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 = multi_log_probs_from_logits_and_actions(
              target_policy_logits, actions)
          behaviour_action_log_probs = multi_log_probs_from_logits_and_actions(
              behaviour_policy_logits, actions)
  
          log_rhos = get_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. 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] 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')
  
              tf.summary.histogram('clipped_rhos_1000', tf.minimum(1000.0, rhos))
              tf.summary.scalar(
                  'num_of_clipped_rhos',
                  tf.reduce_sum(
                      tf.cast(
                          tf.equal(clipped_rhos, clip_rho_threshold), tf.int32)))
              tf.summary.scalar('size_of_clipped_rhos', tf.size(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)
  
          # 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))
  
  
  def get_log_rhos(behaviour_action_log_probs, target_action_log_probs):
      """With the selected log_probs for multi-discrete actions of behaviour
      and target policies we compute the log_rhos for calculating the vtrace."""
      log_rhos = [
          t - b
          for t, b in zip(target_action_log_probs, behaviour_action_log_probs)
      ]
      log_rhos = [tf.convert_to_tensor(l, dtype=tf.float32) for l in log_rhos]
      log_rhos = tf.reduce_sum(tf.stack(log_rhos), axis=0)
  
      return log_rhos
  