code: def train(
      network_def,
      online_params,
      target_params,
      optimizer,
      optimizer_state,
      states,
      actions,
      next_states,
      rewards,
      terminals,
      support,
      cumulative_gamma,
      double_dqn,
      distributional,
      rng,
      bc_coefficient=0.0,
      td_coefficient=1.0,
  ):
      """Run a training step."""
  
      # Split the current rng into 2 for updating the rng after this call
      rng, rng1, rng2 = jax.random.split(rng, num=3)
  
      def q_online(state, key):
          return network_def.apply(
              online_params, state, key=key, support=support
          )
  
      def q_target(state, key):
          return network_def.apply(
              target_params, state, key=key, support=support
          )
  
      def loss_fn(params, target):
          """Computes the distributional loss for C51 or huber loss for DQN."""
  
          def q_func(state, key):
              return network_def.apply(
                  params, state, key=key, support=support
              )
  
          if distributional:
              logits, q_values = get_logits_and_q_values(
                  q_func, states, rng
              )
              # 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
              )
              mean_td_loss = jnp.mean(
                  c51_loss_fn(target, chosen_action_logits)
              )
              replay_chosen_q = jax.vmap(lambda x, y: x[y])(
                  q_values, actions
              )
          else:
              q_values = jnp.squeeze(
                  full_rainbow_agent.get_q_values(q_func, states, rng)
              )
              replay_chosen_q = jax.vmap(lambda x, y: x[y])(
                  q_values, actions
              )
              mean_td_loss = jnp.mean(
                  huber_loss_fn(target, replay_chosen_q)
              )
  
          bc_loss = jnp.mean(
              jax.scipy.special.logsumexp(q_values, axis=-1)
              - replay_chosen_q
          )
          mean_loss = (
              td_coefficient * mean_td_loss + bc_coefficient * bc_loss
          )
          return mean_loss, (mean_td_loss, bc_loss)
  
      target = full_rainbow_agent.target_output(
          q_online,
          q_target,
          next_states,
          rewards,
          terminals,
          support,
          cumulative_gamma,
          double_dqn,
          distributional,
          rng1,
      )
  
      grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
      # Get the unweighted loss without taking its mean for updating priorities.
      # outputs[1] correspond to the per-example TD loss.
      (loss, outputs), grad = grad_fn(online_params, target)
      updates, optimizer_state = optimizer.update(
          grad, optimizer_state, params=online_params
      )
      online_params = optax.apply_updates(online_params, updates)
      return optimizer_state, online_params, loss, outputs, rng2
  
imports: import functools
  from absl import logging
  from dopamine.jax import losses
  from dopamine.jax.agents.full_rainbow import full_rainbow_agent
  from dopamine.jax.agents.rainbow import rainbow_agent
  from dopamine.labs.offline_rl import fixed_replay
  from dopamine.labs.offline_rl.rlu_tfds import tfds_replay
  import gin
  import jax
  import jax.numpy
  import numpy
  import optax
  import tensorflow
label_desc: Use image node_id 2 for calling a global function with example usage: train(network_def, online_params, target_params, optimizer, optimizer_state, states, actions, next_states, rewards, terminals, support, cumulative_gamma, double_dqn, distributional, rng, bc_coefficient, td_coefficient) and returns: optimizer_state,  online_params,  loss,  outputs,  rng2, network_def, network_def, mean_loss,  mean_td_loss,  bc_loss, network_def