text: # coding=utf-8
  # Copyright 2018 The Dopamine Authors.
  #
  # 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
  #
  #      http://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.
  """Compact implementation of a simplified Rainbow agent in Jax.
  
  Specifically, we implement the following components from Rainbow:
  
    * n-step updates;
    * prioritized replay; and
    * distributional RL.
  
  These three components were found to significantly impact the performance of
  the Atari game-playing agent.
  
  Furthermore, our implementation does away with some minor hyperparameter
  choices. Specifically, we
  
    * keep the beta exponent fixed at beta=0.5, rather than increase it linearly;
    * remove the alpha parameter, which was set to alpha=0.5 throughout the paper.
  
  Details in "Rainbow: Combining Improvements in Deep Reinforcement Learning" by
  Hessel et al. (2018).
  """
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import functools
  
  
  
  from dopamine.jax import networks
  from dopamine.jax.agents.dqn import dqn_agent
  from dopamine.replay_memory import prioritized_replay_buffer
  from flax import nn
  import gin
  import jax
  import jax.numpy as jnp
  import tensorflow as tf
  
  
  @functools.partial(jax.jit, static_argnums=(8))
  def train(target_network, optimizer, states, actions, next_states, rewards,
            terminals, support, cumulative_gamma):
    """Run a training step."""
    def loss_fn(model, target, mean_loss=True):
      logits = jax.vmap(model)(states).logits
      logits = jnp.squeeze(logits)
      # Fetch the logits for its selected action. We use vmap to perform this
      # indexing across the batch.
      chosen_action_logits = jax.vmap(lambda x, y: x[y])(logits, actions)
      loss = jax.vmap(networks.softmax_cross_entropy_loss_with_logits)(
          target,
          chosen_action_logits)
      if mean_loss:
        loss = jnp.mean(loss)
      return loss
    grad_fn = jax.value_and_grad(loss_fn)
    target = target_distribution(target_network,
                                 next_states,
                                 rewards,
                                 terminals,
                                 support,
                                 cumulative_gamma)
    mean_loss, grad = grad_fn(optimizer.target, target)
    # Get the loss without taking its mean.
    loss = loss_fn(optimizer.target, target, mean_loss=False)
    optimizer = optimizer.apply_gradient(grad)
    return optimizer, loss, mean_loss
  
  
  @functools.partial(jax.vmap, in_axes=(None, 0, 0, 0, None, None))
  def target_distribution(target_network, next_states, rewards, terminals,
                          support, cumulative_gamma):
    """Builds the C51 target distribution as per Bellemare et al. (2017).
  
    First, we compute the support of the Bellman target, r + gamma Z'. Where Z'
    is the support of the next state distribution:
  
      * Evenly spaced in [-vmax, vmax] if the current state is nonterminal;
      * 0 otherwise (duplicated num_atoms times).
  
    Second, we compute the next-state probabilities, corresponding to the action
    with highest expected value.
  
    Finally we project the Bellman target (support + probabilities) onto the
    original support.
  
    Args:
      target_network: Jax Module used for the target network.
      next_states: numpy array of batched next states.
      rewards: numpy array of batched rewards.
      terminals: numpy array of batched terminals.
      support: support for the distribution (static_argnum).
      cumulative_gamma: float, cumulative gamma to use (static_argnum).
  
    Returns:
      The target distribution from the replay.
    """
    is_terminal_multiplier = 1. - terminals.astype(jnp.float32)
    # Incorporate terminal state to discount factor.
    gamma_with_terminal = cumulative_gamma * is_terminal_multiplier
    target_support = rewards + gamma_with_terminal * support
    next_state_target_outputs = target_network(next_states)
    q_values = jnp.squeeze(next_state_target_outputs.q_values)
    next_qt_argmax = jnp.argmax(q_values)
    probabilities = jnp.squeeze(next_state_target_outputs.probabilities)
    next_probabilities = probabilities[next_qt_argmax]
    return jax.lax.stop_gradient(
        project_distribution(target_support, next_probabilities, support))
  
  
  @gin.configurable
  class JaxRainbowAgent(dqn_agent.JaxDQNAgent):
    """A compact implementation of a simplified Rainbow agent."""
  
    def __init__(self,
                 num_actions,
                 observation_shape=dqn_agent.NATURE_DQN_OBSERVATION_SHAPE,
                 observation_dtype=dqn_agent.NATURE_DQN_DTYPE,
                 stack_size=dqn_agent.NATURE_DQN_STACK_SIZE,
                 network=networks.RainbowNetwork,
                 num_atoms=51,
                 vmin=None,
                 vmax=10.,
                 gamma=0.99,
                 update_horizon=1,
                 min_replay_history=20000,
                 update_period=4,
                 target_update_period=8000,
                 epsilon_fn=dqn_agent.linearly_decaying_epsilon,
                 epsilon_train=0.01,
                 epsilon_eval=0.001,
                 epsilon_decay_period=250000,
                 replay_scheme='prioritized',
                 optimizer='adam',
                 summary_writer=None,
                 summary_writing_frequency=500,
                 allow_partial_reload=False):
      """Initializes the agent and constructs the necessary components.
  
      Args:
        num_actions: int, number of actions the agent can take at any state.
        observation_shape: tuple of ints or an int. If single int, the observation
          is assumed to be a 2D square.
        observation_dtype: DType, specifies the type of the observations. Note
          that if your inputs are continuous, you should set this to jnp.float32.
        stack_size: int, number of frames to use in state stack.
        network: flax.nn Module that is initialized by shape in _create_network
          below. See dopamine.jax.networks.RainbowNetwork as an example.
        num_atoms: int, the number of buckets of the value function distribution.
        vmin: float, the value distribution support is [vmin, vmax]. If None, we
          set it to be -vmax.
        vmax: float, the value distribution support is [vmin, vmax].
        gamma: float, discount factor with the usual RL meaning.
        update_horizon: int, horizon at which updates are performed, the 'n' in
          n-step update.
        min_replay_history: int, number of transitions that should be experienced
          before the agent begins training its value function.
        update_period: int, period between DQN updates.
        target_update_period: int, update period for the target network.
        epsilon_fn: function expecting 4 parameters:
          (decay_period, step, warmup_steps, epsilon). This function should return
          the epsilon value used for exploration during training.
        epsilon_train: float, the value to which the agent's epsilon is eventually
          decayed during training.
        epsilon_eval: float, epsilon used when evaluating the agent.
        epsilon_decay_period: int, length of the epsilon decay schedule.
        replay_scheme: str, 'prioritized' or 'uniform', the sampling scheme of the
          replay memory.
        optimizer: str, name of optimizer to use.
        summary_writer: SummaryWriter object for outputting training statistics.
          Summary writing disabled if set to None.
        summary_writing_frequency: int, frequency with which summaries will be
          written. Lower values will result in slower training.
        allow_partial_reload: bool, whether we allow reloading a partial agent
          (for instance, only the network parameters).
      """
      # We need this because some tools convert round floats into ints.
      vmax = float(vmax)
      self._num_atoms = num_atoms
      # If vmin is not specified, set it to -vmax similar to C51.
      vmin = vmin if vmin else -vmax
      self._support = jnp.linspace(vmin, vmax, num_atoms)
      self._replay_scheme = replay_scheme
  
      super(JaxRainbowAgent, self).__init__(
          num_actions=num_actions,
          observation_shape=observation_shape,
          observation_dtype=observation_dtype,
          stack_size=stack_size,
          network=network.partial(num_atoms=num_atoms,
                                  support=self._support),
          gamma=gamma,
          update_horizon=update_horizon,
          min_replay_history=min_replay_history,
          update_period=update_period,
          target_update_period=target_update_period,
          epsilon_fn=epsilon_fn,
          epsilon_train=epsilon_train,
          epsilon_eval=epsilon_eval,
          epsilon_decay_period=epsilon_decay_period,
          optimizer=optimizer,
          summary_writer=summary_writer,
          summary_writing_frequency=summary_writing_frequency,
          allow_partial_reload=allow_partial_reload)
  
    def _create_network(self, name):
      """Builds a convolutional network that outputs Q-value distributions.
  
      Args:
        name: str, this name is passed to the Jax Module.
      Returns:
        network: Jax Model, the network instantiated by Jax.
      """
      _, initial_params = self.network.init(self._rng,
                                            name=name,
                                            x=self.state,
                                            num_actions=self.num_actions,
                                            num_atoms=self._num_atoms,
                                            support=self._support)
      return nn.Model(self.network, initial_params)
  
    def _build_replay_buffer(self):
      """Creates the replay buffer used by the agent."""
      if self._replay_scheme not in ['uniform', 'prioritized']:
        raise ValueError('Invalid replay scheme: {}'.format(self._replay_scheme))
      # Both replay schemes use the same data structure, but the 'uniform' scheme
      # sets all priorities to the same value (which yields uniform sampling).
      return prioritized_replay_buffer.OutOfGraphPrioritizedReplayBuffer(
          observation_shape=self.observation_shape,
          stack_size=self.stack_size,
          update_horizon=self.update_horizon,
          gamma=self.gamma,
          observation_dtype=self.observation_dtype)
  
    def _train_step(self):
      """Runs a single training step.
  
      Runs training if both:
        (1) A minimum number of frames have been added to the replay buffer.
        (2) `training_steps` is a multiple of `update_period`.
  
      Also, syncs weights from online_network to target_network if training steps
      is a multiple of target update period.
      """
      if self._replay.add_count > self.min_replay_history:
        if self.training_steps % self.update_period == 0:
          self._sample_from_replay_buffer()
          self.optimizer, loss, mean_loss = train(
              self.target_network,
              self.optimizer,
              self.replay_elements['state'],
              self.replay_elements['action'],
              self.replay_elements['next_state'],
              self.replay_elements['reward'],
              self.replay_elements['terminal'],
              self._support,
              self.cumulative_gamma)
          if self._replay_scheme == 'prioritized':
            # The original prioritized experience replay uses a linear exponent
            # schedule 0.4 -> 1.0. Comparing the schedule to a fixed exponent of
            # 0.5 on 5 games (Asterix, Pong, Q*Bert, Seaquest, Space Invaders)
            # suggested a fixed exponent actually performs better, except on Pong.
            probs = self.replay_elements['sampling_probabilities']
            loss_weights = 1.0 / jnp.sqrt(probs + 1e-10)
            loss_weights /= jnp.max(loss_weights)
  
            # Rainbow and prioritized replay are parametrized by an exponent
            # alpha, but in both cases it is set to 0.5 - for simplicity's sake we
            # leave it as is here, using the more direct sqrt(). Taking the square
            # root "makes sense", as we are dealing with a squared loss.  Add a
            # small nonzero value to the loss to avoid 0 priority items. While
            # technically this may be okay, setting all items to 0 priority will
            # cause troubles, and also result in 1.0 / 0.0 = NaN correction terms.
            self._replay.set_priority(self.replay_elements['indices'],
                                      jnp.sqrt(loss + 1e-10))
  
            # Weight the loss by the inverse priorities.
            loss = loss_weights * loss
            mean_loss = jnp.mean(loss)
          if self.summary_writer is not None:
            summary = tf.compat.v1.Summary(value=[
                tf.compat.v1.Summary.Value(tag='CrossEntropyLoss',
                                           simple_value=mean_loss)])
            self.summary_writer.add_summary(summary, self.training_steps)
        if self.training_steps % self.target_update_period == 0:
          self._sync_weights()
  
      self.training_steps += 1
  
  
  def project_distribution(supports, weights, target_support):
    """Projects a batch of (support, weights) onto target_support.
  
    Based on equation (7) in (Bellemare et al., 2017):
      https://arxiv.org/abs/1707.06887
    In the rest of the comments we will refer to this equation simply as Eq7.
  
    Args:
      supports: Jax array of shape (num_dims) defining supports for
        the distribution.
      weights: Jax array of shape (num_dims) defining weights on the
        original support points. Although for the CategoricalDQN agent these
        weights are probabilities, it is not required that they are.
      target_support: Jax array of shape (num_dims) defining support of the
        projected distribution. The values must be monotonically increasing. Vmin
        and Vmax will be inferred from the first and last elements of this Jax
        array, respectively. The values in this Jax array must be equally spaced.
  
    Returns:
      A Jax array of shape (num_dims) with the projection of a batch
      of (support, weights) onto target_support.
  
    Raises:
      ValueError: If target_support has no dimensions, or if shapes of supports,
        weights, and target_support are incompatible.
    """
    v_min, v_max = target_support[0], target_support[-1]
    # `N` in Eq7.
    num_dims = target_support.shape[0]
    # delta_z = `\Delta z` in Eq7.
    delta_z = (v_max - v_min) / (num_dims - 1)
    # clipped_support = `[\hat{T}_{z_j}]^{V_max}_{V_min}` in Eq7.
    clipped_support = jnp.clip(supports, v_min, v_max)
    # numerator = `|clipped_support - z_i|` in Eq7.
    numerator = jnp.abs(clipped_support - target_support[:, None])
    quotient = 1 - (numerator / delta_z)
    # clipped_quotient = `[1 - numerator / (\Delta z)]_0^1` in Eq7.
    clipped_quotient = jnp.clip(quotient, 0, 1)
    # inner_prod = `\sum_{j=0}^{N-1} clipped_quotient * p_j(x', \pi(x'))` in Eq7.
    inner_prod = clipped_quotient * weights
    return jnp.squeeze(jnp.sum(inner_prod, -1))
  