# Copyright 2018 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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"""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)

    sequences = (discounts, cs, deltas)
    # 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,
        reverse=True,  # Computation starts from the back.
        name='scan')

    # 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))
