def compute_grad_knowledge_gradient(self, force_monte_carlo=False):
r"""Compute the gradient of knowledge gradient at ``points_to_sample`` wrt ``points_to_sample``, with ``points_being_sampled`` concurrent samples.
.. Note:: These comments were copied from
:meth:`moe.optimal_learning.python.interfaces.expected_improvement_interface.ExpectedImprovementInterface.compute_grad_expected_improvement`
``points_to_sample`` is the "q" and ``points_being_sampled`` is the "p" in q,p-EI.
In general, the expressions for gradients of EI are complex and difficult to evaluate; hence we use
Monte-Carlo simulation to approximate it. When faster (e.g., analytic) techniques are available, we will prefer them.
The MC computation of grad EI is similar to the computation of EI (decsribed in
compute_expected_improvement). We differentiate ``y = \mu + Lw`` wrt ``points_to_sample``;
only terms from the gradient of ``\mu`` and ``L`` contribute. In EI, we computed:
``improvement_per_step = max(max(best_so_far - y), 0.0)``
and noted that only the smallest component of ``y`` may contribute (if it is > 0.0).
Call this index ``winner``. Thus in computing grad EI, we only add gradient terms
that are attributable to the ``winner``-th component of ``y``.
:param force_monte_carlo: whether to force monte carlo evaluation (vs using fast/accurate analytic eval when possible)
:type force_monte_carlo: boolean
:return: gradient of EI, ``\pderiv{EI(Xq \cup Xp)}{Xq_{i,d}}`` where ``Xq`` is ``points_to_sample``
and ``Xp`` is ``points_being_sampled`` (grad EI from sampling ``points_to_sample`` with
``points_being_sampled`` concurrent experiments wrt each dimension of the points in ``points_to_sample``)
:rtype: array of float64 with shape (num_to_sample, dim)
"""
grad_kg = C_GP.compute_grad_knowledge_gradient(
self._gaussian_process._gaussian_process,
self._num_fidelity,
self._inner_optimizer.optimizer_parameters,
cpp_utils.cppify(self._inner_optimizer.domain.domain_bounds),
cpp_utils.cppify(self._discrete_pts),
cpp_utils.cppify(self._points_to_sample),
cpp_utils.cppify(self._points_being_sampled),
self.discrete,
self.num_to_sample,
self.num_being_sampled,
self._num_mc_iterations,
self._best_so_far,
self._randomness,
)
return cpp_utils.uncppify(grad_kg, (self.num_to_sample, self.dim))
