code: def train(
      network_def: nn.Module,
      optim: optax.GradientTransformation,
      alpha_optim: optax.GradientTransformation,
      optimizer_state: jnp.ndarray,
      alpha_optimizer_state: jnp.ndarray,
      network_params: flax.core.FrozenDict,
      target_params: flax.core.FrozenDict,
      log_alpha: jnp.ndarray,
      key: jnp.ndarray,
      states: jnp.ndarray,
      actions: jnp.ndarray,
      next_states: jnp.ndarray,
      rewards: jnp.ndarray,
      terminals: jnp.ndarray,
      cumulative_gamma: float,
      target_entropy: float,
      reward_scale_factor: float,
  ) -> Mapping[str, Any]:
      """Run the training step.
  
      Returns a list of updated values and losses.
  
      Args:
        network_def: The SAC network definition.
        optim: The SAC optimizer (which also wraps the SAC parameters).
        alpha_optim: The optimizer for alpha.
        optimizer_state: The SAC optimizer state.
        alpha_optimizer_state: The alpha optimizer state.
        network_params: Parameters for SAC's online network.
        target_params: The parameters for SAC's target network.
        log_alpha: Parameters for alpha network.
        key: An rng key to use for random action selection.
        states: A batch of states.
        actions: A batch of actions.
        next_states: A batch of next states.
        rewards: A batch of rewards.
        terminals: A batch of terminals.
        cumulative_gamma: The discount factor to use.
        target_entropy: The target entropy for the agent.
        reward_scale_factor: A factor by which to scale rewards.
  
      Returns:
        A mapping from string keys to values, including updated optimizers and
          training statistics.
      """
      # Get the models from all the optimizers.
      frozen_params = (
          network_params  # For use in loss_fn without apply gradients
      )
  
      batch_size = states.shape[0]
      actions = jnp.reshape(actions, (batch_size, -1))  # Flatten
  
      def loss_fn(
          params: flax.core.FrozenDict,
          log_alpha: flax.core.FrozenDict,
          state: jnp.ndarray,
          action: jnp.ndarray,
          reward: jnp.ndarray,
          next_state: jnp.ndarray,
          terminal: jnp.ndarray,
          rng: jnp.ndarray,
      ) -> Tuple[jnp.ndarray, Mapping[str, jnp.ndarray]]:
          """Calculates the loss for one transition.
  
          Args:
            params: Parameters for the SAC network.
            log_alpha: SAC's log_alpha parameter.
            state: A single state vector.
            action: A single action vector.
            reward: A reward scalar.
            next_state: A next state vector.
            terminal: A terminal scalar.
            rng: An RNG key to use for sampling actions.
  
          Returns:
            A tuple containing 1) the combined SAC loss and 2) a mapping containing
              statistics from the loss step.
          """
          rng1, rng2 = jax.random.split(rng, 2)
  
          # J_Q(\theta) from equation (5) in paper.
          q_value_1, q_value_2 = network_def.apply(
              params, state, action, method=network_def.critic
          )
          q_value_1 = jnp.squeeze(q_value_1)
          q_value_2 = jnp.squeeze(q_value_2)
  
          target_outputs = network_def.apply(
              target_params, next_state, rng1, True
          )
          target_q_value_1, target_q_value_2 = target_outputs.critic
          target_q_value = jnp.squeeze(
              jnp.minimum(target_q_value_1, target_q_value_2)
          )
  
          alpha_value = jnp.exp(
              log_alpha
          )  # pytype: disable=wrong-arg-types  # numpy-scalars
          log_prob = target_outputs.actor.log_probability
          target = reward_scale_factor * reward + cumulative_gamma * (
              target_q_value - alpha_value * log_prob
          ) * (1.0 - terminal)
          target = jax.lax.stop_gradient(target)
          critic_loss_1 = losses.mse_loss(q_value_1, target)
          critic_loss_2 = losses.mse_loss(q_value_2, target)
          critic_loss = jnp.mean(critic_loss_1 + critic_loss_2)
  
          # J_{\pi}(\phi) from equation (9) in paper.
          (
              mean_action,
              sampled_action,
              action_log_prob,
          ) = network_def.apply(
              params, state, rng2, method=network_def.actor
          )
  
          # We use frozen_params so that gradients can flow back to the actor without
          # being used to update the critic.
          q_value_no_grad_1, q_value_no_grad_2 = network_def.apply(
              frozen_params,
              state,
              sampled_action,
              method=network_def.critic,
          )
          no_grad_q_value = jnp.squeeze(
              jnp.minimum(q_value_no_grad_1, q_value_no_grad_2)
          )
          alpha_value = jnp.exp(
              jax.lax.stop_gradient(log_alpha)
          )  # pytype: disable=wrong-arg-types  # numpy-scalars
          policy_loss = jnp.mean(
              alpha_value * action_log_prob - no_grad_q_value
          )
  
          # J(\alpha) from equation (18) in paper.
          entropy_diff = -action_log_prob - target_entropy
          alpha_loss = jnp.mean(
              log_alpha * jax.lax.stop_gradient(entropy_diff)
          )
  
          # Giving a smaller weight to the critic empirically gives better results
          combined_loss = (
              0.5 * critic_loss + 1.0 * policy_loss + 1.0 * alpha_loss
          )
          return combined_loss, {
              "critic_loss": critic_loss,
              "policy_loss": policy_loss,
              "alpha_loss": alpha_loss,
              "critic_value_1": q_value_1,
              "critic_value_2": q_value_2,
              "target_value_1": target_q_value_1,
              "target_value_2": target_q_value_2,
              "mean_action": mean_action,
          }
  
      grad_fn = jax.vmap(
          jax.value_and_grad(loss_fn, argnums=(0, 1), has_aux=True),
          in_axes=(None, None, 0, 0, 0, 0, 0, 0),
      )
  
      rng = jnp.stack(jax.random.split(key, num=batch_size))
      (_, aux_vars), gradients = grad_fn(
          network_params,
          log_alpha,
          states,
          actions,
          rewards,
          next_states,
          terminals,
          rng,
      )
  
      # This calculates the mean gradient/aux_vars using the individual
      # gradients/aux_vars from each item in the batch.
      gradients = jax.tree_map(
          functools.partial(jnp.mean, axis=0), gradients
      )
      aux_vars = jax.tree_map(
          functools.partial(jnp.mean, axis=0), aux_vars
      )
      network_gradient, alpha_gradient = gradients
  
      # Apply gradients to all the optimizers.
      updates, optimizer_state = optim.update(
          network_gradient, optimizer_state, params=network_params
      )
      network_params = optax.apply_updates(network_params, updates)
      alpha_updates, alpha_optimizer_state = alpha_optim.update(
          alpha_gradient, alpha_optimizer_state, params=log_alpha
      )
      log_alpha = optax.apply_updates(log_alpha, alpha_updates)
  
      # Compile everything in a dict.
      returns = {
          "network_params": network_params,
          "log_alpha": log_alpha,
          "optimizer_state": optimizer_state,
          "alpha_optimizer_state": alpha_optimizer_state,
          "Losses/Critic": aux_vars["critic_loss"],
          "Losses/Actor": aux_vars["policy_loss"],
          "Losses/Alpha": aux_vars["alpha_loss"],
          "Values/CriticValues1": jnp.mean(aux_vars["critic_value_1"]),
          "Values/CriticValues2": jnp.mean(aux_vars["critic_value_2"]),
          "Values/TargetValues1": jnp.mean(aux_vars["target_value_1"]),
          "Values/TargetValues2": jnp.mean(aux_vars["target_value_2"]),
          "Values/Alpha": jnp.exp(log_alpha),
      }
      for i, a in enumerate(aux_vars["mean_action"]):
          returns.update({f"Values/MeanActions{i}": a})
      return returns
  
imports: import functools
  import math
  import operator
  import time
  from typing import Any, Mapping, Tuple
  from absl import logging
  from dopamine.jax import continuous_networks
  from dopamine.jax import losses
  from dopamine.jax.agents.dqn import dqn_agent
  import dopamine.labs.sac_from_pixels.continuous_networks
  from dopamine.metrics import statistics_instance
  from dopamine.replay_memory import circular_replay_buffer
  import flax
  from flax import linen
  import gin
  import jax
  import jax.numpy
  import numpy
  import optax
  import tensorflow
label_desc: Use image node_id 1 for calling a global function with example usage: train(network_def, optim, alpha_optim, optimizer_state, alpha_optimizer_state, network_params, target_params, log_alpha, key, states, actions, next_states, rewards, terminals, cumulative_gamma, target_entropy, reward_scale_factor) and returns: returns, combined_loss,  dict