text: import numpy as np
  import random
  import copy
  from collections import namedtuple, deque
  
  from model import Actor, Critic
  
  import torch
  import torch.nn.functional as F
  import torch.optim as optim
  
  BUFFER_SIZE = int(1e6)  # replay buffer size
  BATCH_SIZE = 256        # minibatch size
  GAMMA = 0.99            # discount factor
  TAU = 1e-3              # for soft update of target parameters
  LR_ACTOR = 1e-4         # learning rate of the actor
  LR_CRITIC = 1e-3        # learning rate of the critic
  WEIGHT_DECAY = 0        # L2 weight decay
  LEARN_EVERY = 20        # learning timestep interval
  LEARN_NUM = 10          # number of learning passes
  OU_SIGMA = 0.2          # Ornstein-Uhlenbeck noise parameter
  OU_THETA = 0.15         # Ornstein-Uhlenbeck noise parameter
  
  EPSILON_DECAY = 1e-6   # noise reduction -> Similar to greedy reduction eploration and exploiting
  EPSILON       = 1.0    # Initial noise reduction level
  
  device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
  
  class Agent():
      """Interacts with and learns from the environment."""
  
      def __init__(self, state_size, action_size, random_seed):
          """Initialize an Agent object.
  
          Params
          ======
              state_size (int): dimension of each state
              action_size (int): dimension of each action
              random_seed (int): random seed
          """
          self.state_size = state_size
          self.action_size = action_size
          self.seed = random.seed(random_seed)
  
          # Actor Network (w/ Target Network)
          self.actor_local = Actor(state_size, action_size, random_seed).to(device)
          self.actor_target = Actor(state_size, action_size, random_seed).to(device)
          self.actor_optimizer = optim.Adam(self.actor_local.parameters(), lr=LR_ACTOR)
  
          # Critic Network (w/ Target Network)
          self.critic_local = Critic(state_size, action_size, random_seed).to(device)
          self.critic_target = Critic(state_size, action_size, random_seed).to(device)
          self.critic_optimizer = optim.Adam(self.critic_local.parameters(), lr=LR_CRITIC, weight_decay=WEIGHT_DECAY)
  
          # Noise process
          self.noise = OUNoise(action_size, random_seed)
          self.epsilon = EPSILON 
  
          # Replay memory
          self.memory = ReplayBuffer(action_size, BUFFER_SIZE, BATCH_SIZE, random_seed)
  
      def step(self, states, actions, rewards, next_states, dones, t):
          """Save experience in replay memory, and use random sample from buffer to learn."""
          # Save experience / reward
          for state, action, reward, next_state, done in zip(states, actions, rewards, next_states, dones):
              self.memory.add(state, action, reward, next_state, done)
      
          # Learn, if enough samples are available in memory
          if (len(self.memory) > BATCH_SIZE) and ((t % LEARN_EVERY) == 0):
              for _ in range(LEARN_NUM):
                  experiences = self.memory.sample()
                  self.learn(experiences, GAMMA)
  
      def act(self, state, add_noise=True):
          """Returns actions for given state as per current policy."""
          state = torch.from_numpy(state).float().to(device)
          self.actor_local.eval()
          with torch.no_grad():
              action = self.actor_local(state).cpu().data.numpy()
          self.actor_local.train()
          if add_noise:
              self.epsilon  -= EPSILON_DECAY
              #action += self.noise.sample()
              action +=  np.maximum(self.epsilon,0.01) * self.noise.sample()  # Andding Nois for exploration in off-policy environment
          return np.clip(action, -1, 1)
  
      def reset(self):
          self.noise.reset()
  
      def learn(self, experiences, gamma):
          """Update policy and value parameters using given batch of experience tuples.
          Q_targets = r + γ * critic_target(next_state, actor_target(next_state))
          where:
              actor_target(state) -> action
              critic_target(state, action) -> Q-value
  
          Params
          ======
              experiences (Tuple[torch.Tensor]): tuple of (s, a, r, s', done) tuples
              gamma (float): discount factor
          """
          states, actions, rewards, next_states, dones = experiences
  
          # ---------------------------- update critic ---------------------------- #
          # Get predicted next-state actions and Q values from target models
          actions_next = self.actor_target(next_states)
          Q_targets_next = self.critic_target(next_states, actions_next)
          # Compute Q targets for current states (y_i)
          Q_targets = rewards + (gamma * Q_targets_next * (1 - dones))
          # Compute critic loss
          Q_expected = self.critic_local(states, actions)
          critic_loss = F.mse_loss(Q_expected, Q_targets)
          # Minimize the loss
          self.critic_optimizer.zero_grad()
          critic_loss.backward()
          torch.nn.utils.clip_grad_norm_(self.critic_local.parameters(), 1)
          self.critic_optimizer.step()
  
          # ---------------------------- update actor ---------------------------- #
          # Compute actor loss
          actions_pred = self.actor_local(states)
          actor_loss = -self.critic_local(states, actions_pred).mean() # gradient ascent
          # Minimize the loss
          self.actor_optimizer.zero_grad()
          actor_loss.backward()
          self.actor_optimizer.step()
  
          # ----------------------- update target networks ----------------------- #
          self.soft_update(self.critic_local, self.critic_target, TAU)
          self.soft_update(self.actor_local, self.actor_target, TAU)
  
      def soft_update(self, local_model, target_model, tau):
          """Soft update model parameters.
          θ_target = τ*θ_local + (1 - τ)*θ_target
  
          Params
          ======
              local_model: PyTorch model (weights will be copied from)
              target_model: PyTorch model (weights will be copied to)
              tau (float): interpolation parameter
          """
          for target_param, local_param in zip(target_model.parameters(), local_model.parameters()):
              target_param.data.copy_(tau*local_param.data + (1.0-tau)*target_param.data)
  
  class OUNoise:
      """Ornstein-Uhlenbeck process."""
  
      def __init__(self, size, seed, mu=0., theta=0.15, sigma=0.2):
          """Initialize parameters and noise process."""
          self.mu = mu * np.ones(size)
          self.theta = theta
          self.sigma = sigma
          self.seed = random.seed(seed)
          self.reset()
  
      def reset(self):
          """Reset the internal state (= noise) to mean (mu)."""
          self.state = copy.copy(self.mu)
  
      def sample(self):
          """Update internal state and return it as a noise sample."""
          x = self.state
          dx = self.theta * (self.mu - x) + self.sigma * np.array([random.random() for i in range(len(x))])
          self.state = x + dx
          return self.state
  
  class ReplayBuffer:
      """Fixed-size buffer to store experience tuples."""
  
      def __init__(self, action_size, buffer_size, batch_size, seed):
          """Initialize a ReplayBuffer object.
          Params
          ======
              buffer_size (int): maximum size of buffer
              batch_size (int): size of each training batch
          """
          self.action_size = action_size
          self.memory = deque(maxlen=buffer_size)  # internal memory (deque)
          self.batch_size = batch_size
          self.experience = namedtuple("Experience", field_names=["state", "action", "reward", "next_state", "done"])
          self.seed = random.seed(seed)
  
      def add(self, state, action, reward, next_state, done):
          """Add a new experience to memory."""
          e = self.experience(state, action, reward, next_state, done)
          self.memory.append(e)
  
      def sample(self):
          """Randomly sample a batch of experiences from memory."""
          experiences = random.sample(self.memory, k=self.batch_size)
  
          states = torch.from_numpy(np.vstack([e.state for e in experiences if e is not None])).float().to(device)
          actions = torch.from_numpy(np.vstack([e.action for e in experiences if e is not None])).float().to(device)
          rewards = torch.from_numpy(np.vstack([e.reward for e in experiences if e is not None])).float().to(device)
          next_states = torch.from_numpy(np.vstack([e.next_state for e in experiences if e is not None])).float().to(device)
          dones = torch.from_numpy(np.vstack([e.done for e in experiences if e is not None]).astype(np.uint8)).float().to(device)
  
          return (states, actions, rewards, next_states, dones)
  
      def __len__(self):
          """Return the current size of internal memory."""
          return len(self.memory)
  