code: def _test_compute_loss_with_kl_constraint(base_policy):
      # Train a policy with and without KL constraint against the original
      # distribution to confirm KL constraint works.
  
      x = torch.rand(1, 1)
  
      with torch.no_grad():
          # Compute KL divergence against the original distribution
          base_distrib = base_policy(x)
  
      def base_loss_func(distrib):
          # Any loss that tends to increase KL divergence should be ok
          kl = torch.distributions.kl_divergence(base_distrib, distrib)
          return -(kl + distrib.entropy())
  
      def compute_kl_after_update(loss_func, n=100):
          policy = copy.deepcopy(base_policy)
          optimizer = torch.optim.SGD(policy.parameters(), 1e-2)
          for _ in range(n):
              distrib = policy(x)
              policy.zero_grad()
              loss_func(distrib).backward(retain_graph=True)
              optimizer.step()
          with torch.no_grad():
              distrib_after = policy(x)
              return float(
                  torch.distributions.kl_divergence(
                      base_distrib, distrib_after
                  )
              )
  
      # Without kl constraint
      kl_after_without_constraint = compute_kl_after_update(
          base_loss_func
      )
      print("kl_after_without_constraint", kl_after_without_constraint)
  
      # With kl constraint
      def loss_func_with_constraint(distrib):
          loss, kl = acer.compute_loss_with_kl_constraint(
              distrib, base_distrib, base_loss_func(distrib), delta=0
          )
          return loss
  
      kl_after_with_constraint = compute_kl_after_update(
          loss_func_with_constraint
      )
      print("kl_after_with_constraint", kl_after_with_constraint)
  
      # KL constraint should make KL divergence small after updates
      assert kl_after_with_constraint < kl_after_without_constraint
  
imports: import copy
  import logging
  import os
  import tempfile
  import warnings
  import numpy
  import pytest
  import torch
  from torch import nn
  import pfrl
  from pfrl.agents import acer
  from pfrl.envs.abc import ABC
  from pfrl.experiments.evaluator import run_evaluation_episodes
  from pfrl.experiments.train_agent_async import train_agent_async
  from pfrl.nn import ConcatObsAndAction
  from pfrl.policies import GaussianHeadWithDiagonalCovariance, SoftmaxCategoricalHead
  from pfrl.q_functions import DiscreteActionValueHead
  from pfrl.replay_buffers import EpisodicReplayBuffer
label_desc: Use image node_id 7 for calling a global function with example usage: _test_compute_loss_with_kl_constraint(base_policy) and returns: unknown, loss, float