def ucb_sub(mu, std, beta=3.):
  """Sub function to compute the upper confidence bound acquisition function.

  Args:
    mu: n x 1 posterior mean of n query points.
    std: n x 1 posterior standard deviation of n query points (same order as
      mu).
    beta: scaling parameter between mean and standard deviation in UCB
      acquisition function. Default value is 3.

  Returns:
    Upper confidence bound.
  """
  return mu + beta * std