text: import torch as th
  import torch.nn.functional as F
  from typing import List, Tuple, Type, Union, Callable, Optional, Dict, Any
  
  from stable_baselines3.common import logger
  from stable_baselines3.common.off_policy_algorithm import OffPolicyAlgorithm
  from stable_baselines3.common.noise import ActionNoise
  from stable_baselines3.common.type_aliases import GymEnv, MaybeCallback
  from stable_baselines3.td3.policies import TD3Policy
  
  
  class TD3(OffPolicyAlgorithm):
      """
      Twin Delayed DDPG (TD3)
      Addressing Function Approximation Error in Actor-Critic Methods.
  
      Original implementation: https://github.com/sfujim/TD3
      Paper: https://arxiv.org/abs/1802.09477
      Introduction to TD3: https://spinningup.openai.com/en/latest/algorithms/td3.html
  
      :param policy: (TD3Policy or str) The policy model to use (MlpPolicy, CnnPolicy, ...)
      :param env: (GymEnv or str) The environment to learn from (if registered in Gym, can be str)
      :param learning_rate: (float or callable) learning rate for adam optimizer,
          the same learning rate will be used for all networks (Q-Values, Actor and Value function)
          it can be a function of the current progress remaining (from 1 to 0)
      :param buffer_size: (int) size of the replay buffer
      :param learning_starts: (int) how many steps of the model to collect transitions for before learning starts
      :param batch_size: (int) Minibatch size for each gradient update
      :param tau: (float) the soft update coefficient ("Polyak update", between 0 and 1)
      :param gamma: (float) the discount factor
      :param train_freq: (int) Update the model every ``train_freq`` steps.
      :param gradient_steps: (int) How many gradient update after each step
      :param n_episodes_rollout: (int) Update the model every ``n_episodes_rollout`` episodes.
          Note that this cannot be used at the same time as ``train_freq``
      :param action_noise: (ActionNoise) the action noise type (None by default), this can help
          for hard exploration problem. Cf common.noise for the different action noise type.
      :param policy_delay: (int) Policy and target networks will only be updated once every policy_delay steps
          per training steps. The Q values will be updated policy_delay more often (update every training step).
      :param target_policy_noise: (float) Standard deviation of Gaussian noise added to target policy
          (smoothing noise)
      :param target_noise_clip: (float) Limit for absolute value of target policy smoothing noise.
      :param create_eval_env: (bool) Whether to create a second environment that will be
          used for evaluating the agent periodically. (Only available when passing string for the environment)
      :param policy_kwargs: (dict) additional arguments to be passed to the policy on creation
      :param verbose: (int) the verbosity level: 0 no output, 1 info, 2 debug
      :param seed: (int) Seed for the pseudo random generators
      :param device: (str or th.device) Device (cpu, cuda, ...) on which the code should be run.
          Setting it to auto, the code will be run on the GPU if possible.
      :param _init_setup_model: (bool) Whether or not to build the network at the creation of the instance
      """
  
      def __init__(self, policy: Union[str, Type[TD3Policy]],
                   env: Union[GymEnv, str],
                   learning_rate: Union[float, Callable] = 1e-3,
                   buffer_size: int = int(1e6),
                   learning_starts: int = 100,
                   batch_size: int = 100,
                   tau: float = 0.005,
                   gamma: float = 0.99,
                   train_freq: int = -1,
                   gradient_steps: int = -1,
                   n_episodes_rollout: int = 1,
                   action_noise: Optional[ActionNoise] = None,
                   policy_delay: int = 2,
                   target_policy_noise: float = 0.2,
                   target_noise_clip: float = 0.5,
                   tensorboard_log: Optional[str] = None,
                   create_eval_env: bool = False,
                   policy_kwargs: Dict[str, Any] = None,
                   verbose: int = 0,
                   seed: Optional[int] = None,
                   device: Union[th.device, str] = 'auto',
                   _init_setup_model: bool = True):
  
          super(TD3, self).__init__(policy, env, TD3Policy, learning_rate,
                                    buffer_size, learning_starts, batch_size,
                                    policy_kwargs, tensorboard_log, verbose, device,
                                    create_eval_env=create_eval_env, seed=seed,
                                    sde_support=False)
  
          self.train_freq = train_freq
          self.gradient_steps = gradient_steps
          self.n_episodes_rollout = n_episodes_rollout
          self.tau = tau
          self.gamma = gamma
          self.action_noise = action_noise
          self.policy_delay = policy_delay
          self.target_noise_clip = target_noise_clip
          self.target_policy_noise = target_policy_noise
  
          if _init_setup_model:
              self._setup_model()
  
      def _setup_model(self) -> None:
          super(TD3, self)._setup_model()
          self._create_aliases()
  
      def _create_aliases(self) -> None:
          self.actor = self.policy.actor
          self.actor_target = self.policy.actor_target
          self.critic = self.policy.critic
          self.critic_target = self.policy.critic_target
  
      def train(self, gradient_steps: int, batch_size: int = 100, policy_delay: int = 2) -> None:
  
          # Update learning rate according to lr schedule
          self._update_learning_rate([self.actor.optimizer, self.critic.optimizer])
  
          for gradient_step in range(gradient_steps):
  
              # Sample replay buffer
              replay_data = self.replay_buffer.sample(batch_size, env=self._vec_normalize_env)
  
              with th.no_grad():
                  # Select action according to policy and add clipped noise
                  noise = replay_data.actions.clone().data.normal_(0, self.target_policy_noise)
                  noise = noise.clamp(-self.target_noise_clip, self.target_noise_clip)
                  next_actions = (self.actor_target(replay_data.next_observations) + noise).clamp(-1, 1)
  
                  # Compute the target Q value
                  target_q1, target_q2 = self.critic_target(replay_data.next_observations, next_actions)
                  target_q = th.min(target_q1, target_q2)
                  target_q = replay_data.rewards + (1 - replay_data.dones) * self.gamma * target_q
  
              # Get current Q estimates
              current_q1, current_q2 = self.critic(replay_data.observations, replay_data.actions)
  
              # Compute critic loss
              critic_loss = F.mse_loss(current_q1, target_q) + F.mse_loss(current_q2, target_q)
  
              # Optimize the critic
              self.critic.optimizer.zero_grad()
              critic_loss.backward()
              self.critic.optimizer.step()
  
              # Delayed policy updates
              if gradient_step % policy_delay == 0:
                  # Compute actor loss
                  actor_loss = -self.critic.q1_forward(replay_data.observations,
                                                       self.actor(replay_data.observations)).mean()
  
                  # Optimize the actor
                  self.actor.optimizer.zero_grad()
                  actor_loss.backward()
                  self.actor.optimizer.step()
  
                  # Update the frozen target networks
                  for param, target_param in zip(self.critic.parameters(), self.critic_target.parameters()):
                      target_param.data.copy_(self.tau * param.data + (1 - self.tau) * target_param.data)
  
                  for param, target_param in zip(self.actor.parameters(), self.actor_target.parameters()):
                      target_param.data.copy_(self.tau * param.data + (1 - self.tau) * target_param.data)
  
          self._n_updates += gradient_steps
          logger.record("train/n_updates", self._n_updates, exclude='tensorboard')
  
      def learn(self,
                total_timesteps: int,
                callback: MaybeCallback = None,
                log_interval: int = 4,
                eval_env: Optional[GymEnv] = None,
                eval_freq: int = -1,
                n_eval_episodes: int = 5,
                tb_log_name: str = "TD3",
                eval_log_path: Optional[str] = None,
                reset_num_timesteps: bool = True) -> OffPolicyAlgorithm:
  
          total_timesteps, callback = self._setup_learn(total_timesteps, eval_env, callback, eval_freq,
                                                        n_eval_episodes, eval_log_path, reset_num_timesteps,
                                                        tb_log_name)
          callback.on_training_start(locals(), globals())
  
          while self.num_timesteps < total_timesteps:
  
              rollout = self.collect_rollouts(self.env, n_episodes=self.n_episodes_rollout,
                                              n_steps=self.train_freq, action_noise=self.action_noise,
                                              callback=callback,
                                              learning_starts=self.learning_starts,
                                              replay_buffer=self.replay_buffer,
                                              log_interval=log_interval)
  
              if rollout.continue_training is False:
                  break
  
              self._update_current_progress_remaining(self.num_timesteps, total_timesteps)
  
              if self.num_timesteps > 0 and self.num_timesteps > self.learning_starts:
                  gradient_steps = self.gradient_steps if self.gradient_steps > 0 else rollout.episode_timesteps
                  self.train(gradient_steps, batch_size=self.batch_size, policy_delay=self.policy_delay)
  
          callback.on_training_end()
  
          return self
  
      def excluded_save_params(self) -> List[str]:
          """
          Returns the names of the parameters that should be excluded by default
          when saving the model.
  
          :return: (List[str]) List of parameters that should be excluded from save
          """
          # Exclude aliases
          return super(TD3, self).excluded_save_params() + ["actor", "critic", "actor_target", "critic_target"]
  
      def get_torch_variables(self) -> Tuple[List[str], List[str]]:
          """
          cf base class
          """
          state_dicts = ["policy", "actor.optimizer", "critic.optimizer"]
          return state_dicts, []
  