text: import numpy as np
  import random
  from collections import namedtuple, deque
  
  from model import QNetwork
  
  import torch
  import torch.nn.functional as F
  import torch.optim as optim
  
  BUFFER_SIZE = int(1e5)  # replay buffer size
  BATCH_SIZE = 64         # minibatch size for learning
  GAMMA = 0.99            # discount factor
  TAU = 1e-3              # for soft update of target parameters
  LR = 5e-4               # learning rate 
  UPDATE_EVERY = 4        # how often to update the network
  
  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, seed):
          """Initialize an Agent object.
          
          Params
          ======
              state_size (int): dimension of each state
              action_size (int): dimension of each action
              seed (int): random seed
          """
          self.state_size = state_size
          self.action_size = action_size
          self.seed = random.seed(seed)
  
          # Q-Network
          # Create the network, define the criterion and optimizer
          hidden_layers = [37, 37]
          self.qnetwork_local = QNetwork(state_size, action_size, hidden_layers, seed).to(device)
          self.qnetwork_target = QNetwork(state_size, action_size, hidden_layers, seed).to(device)
          self.optimizer = optim.Adam(self.qnetwork_local.parameters(), lr=LR)
  
          # Replay memory
          self.memory = ReplayBuffer(action_size, BUFFER_SIZE, BATCH_SIZE, seed)
          # Initialize time step (for updating every UPDATE_EVERY steps)
          self.t_step = 0
      
      def step(self, state, action, reward, next_state, done):
          # Save experience in replay memory
          self.memory.add(state, action, reward, next_state, done)
          
          # Learn every UPDATE_EVERY time steps.
          self.t_step = (self.t_step + 1) % UPDATE_EVERY
          if self.t_step == 0:
              # If enough samples are available in memory, get random subset and learn
              if len(self.memory) > BATCH_SIZE:
                  experiences = self.memory.sample()
                  self.learn(experiences, GAMMA)
  
      def act(self, state, eps=0.):
          """Returns actions for given state as per current policy.
          
          Params
          ======
              state (array_like): current state
              eps (float): epsilon, for epsilon-greedy action selection
          """
          state = torch.from_numpy(state).float().unsqueeze(0).to(device)
          self.qnetwork_local.eval()
          with torch.no_grad():
              action_values = self.qnetwork_local(state)
          self.qnetwork_local.train()
  
          # Epsilon-greedy action selection
          if random.random() > eps:
              return np.argmax(action_values.cpu().data.numpy())
          else:
              return random.choice(np.arange(self.action_size))
  
      def learn(self, experiences, gamma):
          """Update value parameters using given batch of experience tuples.
  
          Params
          ======
              experiences (Tuple[torch.Tensor]): tuple of (s, a, r, s', done) tuples 
              gamma (float): discount factor
          """
          states, actions, rewards, next_states, dones = experiences
  
          # Get max predicted Q values (for next states) from target model
          Q_targets_next = self.qnetwork_target(next_states).detach().max(1)[0].unsqueeze(1)
          # Compute Q targets for current states 
          Q_targets = rewards + (gamma * Q_targets_next * (1 - dones))
  
          # Get expected Q values from local model
          Q_expected = self.qnetwork_local(states).gather(1, actions)
  
          # Compute loss
          loss = F.mse_loss(Q_expected, Q_targets)
          # Minimize the loss
          self.optimizer.zero_grad()
          loss.backward()
          self.optimizer.step()
  
          # ------------------- update target network ------------------- #
          self.soft_update(self.qnetwork_local, self.qnetwork_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 ReplayBuffer:
      """Fixed-size buffer to store experience tuples."""
  
      def __init__(self, action_size, buffer_size, batch_size, seed):
          """Initialize a ReplayBuffer object.
  
          Params
          ======
              action_size (int): dimension of each action
              buffer_size (int): maximum size of buffer
              batch_size (int): size of each training batch
              seed (int): random seed
          """
          self.action_size = action_size
          self.memory = deque(maxlen=buffer_size)  
          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])).long().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)