code: def learn_from_batch(self, batch):
      network_keys = self.ap.network_wrappers[
          "main"
      ].input_embedders_parameters.keys()
  
      # for the action we actually took, the error is calculated by the atoms distribution
      # for all other actions, the error is 0
      distributional_q_st_plus_1, TD_targets = self.networks[
          "main"
      ].parallel_prediction(
          [
              (
                  self.networks["main"].target_network,
                  batch.next_states(network_keys),
              ),
              (
                  self.networks["main"].online_network,
                  batch.states(network_keys),
              ),
          ]
      )
  
      # add Q value samples for logging
      self.q_values.add_sample(
          self.distribution_prediction_to_q_values(TD_targets)
      )
  
      # select the optimal actions for the next state
      target_actions = np.argmax(
          self.distribution_prediction_to_q_values(
              distributional_q_st_plus_1
          ),
          axis=1,
      )
      m = np.zeros((batch.size, self.z_values.size))
  
      batches = np.arange(batch.size)
  
      # an alternative to the for loop. 3.7x perf improvement vs. the same code done with for looping.
      # only 10% speedup overall - leaving commented out as the code is not as clear.
  
      # tzj_ = np.fmax(np.fmin(batch.rewards() + (1.0 - batch.game_overs()) * self.ap.algorithm.discount *
      #                        np.transpose(np.repeat(self.z_values[np.newaxis, :], batch.size, axis=0), (1, 0)),
      #                     self.z_values[-1]),
      #             self.z_values[0])
      #
      # bj_ = (tzj_ - self.z_values[0]) / (self.z_values[1] - self.z_values[0])
      # u_ = (np.ceil(bj_)).astype(int)
      # l_ = (np.floor(bj_)).astype(int)
      # m_ = np.zeros((batch.size, self.z_values.size))
      # np.add.at(m_, [batches, l_],
      #           np.transpose(distributional_q_st_plus_1[batches, target_actions], (1, 0)) * (u_ - bj_))
      # np.add.at(m_, [batches, u_],
      #           np.transpose(distributional_q_st_plus_1[batches, target_actions], (1, 0)) * (bj_ - l_))
  
      for j in range(self.z_values.size):
          tzj = np.fmax(
              np.fmin(
                  batch.rewards()
                  + (1.0 - batch.game_overs())
                  * self.ap.algorithm.discount
                  * self.z_values[j],
                  self.z_values[-1],
              ),
              self.z_values[0],
          )
          bj = (tzj - self.z_values[0]) / (
              self.z_values[1] - self.z_values[0]
          )
          u = (np.ceil(bj)).astype(int)
          l = (np.floor(bj)).astype(int)
          m[batches, l] += distributional_q_st_plus_1[
              batches, target_actions, j
          ] * (u - bj)
          m[batches, u] += distributional_q_st_plus_1[
              batches, target_actions, j
          ] * (bj - l)
  
      # total_loss = cross entropy between actual result above and predicted result for the given action
      # only update the action that we have actually done in this transition
      TD_targets[batches, batch.actions()] = m
  
      # update errors in prioritized replay buffer
      importance_weights = (
          batch.info("weight")
          if isinstance(self.memory, PrioritizedExperienceReplay)
          else None
      )
  
      result = self.networks["main"].train_and_sync_networks(
          batch.states(network_keys),
          TD_targets,
          importance_weights=importance_weights,
      )
  
      total_loss, losses, unclipped_grads = result[:3]
  
      # TODO: fix this spaghetti code
      if isinstance(self.memory, PrioritizedExperienceReplay):
          errors = losses[0][np.arange(batch.size), batch.actions()]
          self.call_memory(
              "update_priorities", (batch.info("idx"), errors)
          )
  
      return total_loss, losses, unclipped_grads
  
imports: from typing import Union
  import numpy
  from rl_coach.agents.dqn_agent import DQNNetworkParameters, DQNAlgorithmParameters, DQNAgentParameters
  from rl_coach.agents.value_optimization_agent import ValueOptimizationAgent
  from rl_coach.architectures.head_parameters import CategoricalQHeadParameters
  from rl_coach.core_types import StateType
  from rl_coach.exploration_policies.e_greedy import EGreedyParameters
  from rl_coach.memories.non_episodic.prioritized_experience_replay import PrioritizedExperienceReplay
  from rl_coach.schedules import LinearSchedule
label_desc: Use image node_id 6 for calling the CategoricalDQNAgent obj's underlying member method code with example usage: obj.learn_from_batch(batch) and returns: total_loss,  losses,  unclipped_grads