def sarsa(q_tm1, a_tm1, r_t, pcont_t, q_t, a_t, name="Sarsa"):
  """Implements the SARSA loss as a TensorFlow op.

  The loss is `0.5` times the squared difference between `q_tm1[a_tm1]` and
  the target `r_t + pcont_t * q_t[a_t]`.

  See "Reinforcement Learning: An Introduction" by Sutton and Barto.
  (http://incompleteideas.net/book/ebook/node64.html.)

  Args:
    q_tm1: Tensor holding Q-values for first timestep in a batch of
      transitions, shape `[B x num_actions]`.
    a_tm1: Tensor holding action indices, shape `[B]`.
    r_t: Tensor holding rewards, shape `[B]`.
    pcont_t: Tensor holding pcontinue values, shape `[B]`.
    q_t: Tensor holding Q-values for second timestep in a batch of
      transitions, shape `[B x num_actions]`.
    a_t: Tensor holding action indices for second timestep, shape `[B]`.
    name: name to prefix ops created within this op.

  Returns:
    A namedtuple with fields:

    * `loss`: a tensor containing the batch of losses, shape `[B]`.
    * `extra`: a namedtuple with fields:
        * `target`: batch of target values for `q_tm1[a_tm1]`, shape `[B]`.
        * `td_error`: batch of temporal difference errors, shape `[B]`.
  """
  # Rank and compatibility checks.
  base_ops.wrap_rank_shape_assert(
      [[q_tm1, q_t], [a_t, r_t, pcont_t]], [2, 1], name)

  # SARSA op.
  with tf.name_scope(name, values=[q_tm1, a_tm1, r_t, pcont_t, q_t, a_t]):

    # Select head to update and build target.
    qa_tm1 = indexing_ops.batched_index(q_tm1, a_tm1)
    qa_t = indexing_ops.batched_index(q_t, a_t)
    target = tf.stop_gradient(r_t + pcont_t * qa_t)

    # Temporal difference error and loss.
    # Loss is MSE scaled by 0.5, so the gradient is equal to the TD error.
    td_error = target - qa_tm1
    loss = 0.5 * tf.square(td_error)
    return base_ops.LossOutput(loss, QExtra(target, td_error))
Implements the SARSA loss as a TensorFlow op.

  The loss is `0.5` times the squared difference between `q_tm1[a_tm1]` and
  the target `r_t + pcont_t * q_t[a_t]`.

  See "Reinforcement Learning: An Introduction" by Sutton and Barto.
  (http://incompleteideas.net/book/ebook/node64.html.)

  Args:
    q_tm1: Tensor holding Q-values for first timestep in a batch of
      transitions, shape `[B x num_actions]`.
    a_tm1: Tensor holding action indices, shape `[B]`.
    r_t: Tensor holding rewards, shape `[B]`.
    pcont_t: Tensor holding pcontinue values, shape `[B]`.
    q_t: Tensor holding Q-values for second timestep in a batch of
      transitions, shape `[B x num_actions]`.
    a_t: Tensor holding action indices for second timestep, shape `[B]`.
    name: name to prefix ops created within this op.

  Returns:
    A namedtuple with fields:

    * `loss`: a tensor containing the batch of losses, shape `[B]`.
    * `extra`: a namedtuple with fields:
        * `target`: batch of target values for `q_tm1[a_tm1]`, shape `[B]`.
        * `td_error`: batch of temporal difference errors, shape `[B]`.
  
trfl/action_value_ops.py