def dueling_model(img_in, num_actions, scope, noisy=False, reuse=False,
                  concat_softmax=False):
  """As described in https://arxiv.org/abs/1511.06581"""
  with tf.variable_scope(scope, reuse=reuse):
    out = img_in
    with tf.variable_scope("convnet"):
      # original architecture
      out = layers.convolution2d(out, num_outputs=32, kernel_size=8,
                                 stride=4, activation_fn=tf.nn.relu)
      out = layers.convolution2d(out, num_outputs=64, kernel_size=4,
                                 stride=2, activation_fn=tf.nn.relu)
      out = layers.convolution2d(out, num_outputs=64, kernel_size=3,
                                 stride=1, activation_fn=tf.nn.relu)
    out = layers.flatten(out)

    with tf.variable_scope("state_value"):
      if noisy:
        # Apply noisy network on fully connected layers
        # ref: https://arxiv.org/abs/1706.10295
        state_hidden = noisy_dense(out, name='noisy_fc1', size=512,
                                   activation_fn=tf.nn.relu)
        state_score = noisy_dense(state_hidden, name='noisy_fc2',
                                  size=1)
      else:
        state_hidden = layers.fully_connected(
            out,
            num_outputs=512,
            activation_fn=tf.nn.relu
        )
        state_score = layers.fully_connected(state_hidden,
                                             num_outputs=1,
                                             activation_fn=None)
    with tf.variable_scope("action_value"):
      if noisy:
        # Apply noisy network on fully connected layers
        # ref: https://arxiv.org/abs/1706.10295
        actions_hidden = noisy_dense(out, name='noisy_fc1', size=512,
                                     activation_fn=tf.nn.relu)
        action_scores = noisy_dense(actions_hidden, name='noisy_fc2',
                                    size=num_actions)
      else:
        actions_hidden = layers.fully_connected(
            out,
            num_outputs=512,
            activation_fn=tf.nn.relu
        )
        action_scores = layers.fully_connected(
            actions_hidden,
            num_outputs=num_actions,
            activation_fn=None
        )
      action_scores_mean = tf.reduce_mean(action_scores, 1)
      action_scores = action_scores - tf.expand_dims(
          action_scores_mean,
          1
      )

    return state_score + action_scores