Adds the Dynamic NLCB acquisition as an example (#332)

* Adds the Dynamic NLCB acquisition as an example

* Adds a toy example

Co-authored-by: Andrei Paleyes <apaleyes@users.noreply.github.com>

emukit/examples/dynamic_negative_lower_confidence_bound/__init__.py

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+from .dnlcb import DynamicNegativeLowerConfidenceBound

emukit/examples/dynamic_negative_lower_confidence_bound/dnlcb.py

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+from emukit.bayesian_optimization.acquisitions import NegativeLowerConfidenceBound
+from emukit.core.interfaces import IModel, IDifferentiable
+import numpy as np
+from typing import Union
+
+class DynamicNegativeLowerConfidenceBound(NegativeLowerConfidenceBound):
+
+    def __init__(self, model: Union[IModel, IDifferentiable], input_space_size: int, delta: float) -> None:
+        """
+        Dynamic extension of the LCB acquisition. The beta coefficient is updated at each iteration, based on the explorativeness parameter delta which is inversely
+        proportional to beta itself - the higher the delta the less explorative the selection will be.
+        Please consider that regret bounds based on the dynamic exploration coefficient only hold for selected kernel classes exhibiting boundedness and smoothness.
+        See the base class for paper references.
+        This class may also be taken as a reference for acquisition functions that dynamically update their parameters thanks to the update_parameters() hook; the implicit assumption is that this method is invoked once per iteration (it is no big deal if this is the case for a constant number of times per iteration; should it be more then we are increasing the beta too fast).
+        :param model: The underlying model that provides the predictive mean and variance for the given test points
+        :param input_space_size: the size of the finite D grid on which the function is evaluated
+        :param delta: the exploration parameter determining the beta exploration coefficient; delta must be in (0, 1) and it is inversely related to beta
+        """
+        assert input_space_size > 0, "Invalid dimension provided"
+        assert 0 < delta < 1, "Delta must be in (0, 1)"
+        super().__init__(model)
+        self.input_space_size = input_space_size
+        self.delta = delta
+        self.iteration = 0
+
+    def optimal_beta_selection(self) -> float:
+        return 2 * np.log(self.input_space_size * (self.iteration ** 2) * (np.pi ** 2) / (6 * self.delta))
+
+    def update_parameters(self) -> None:
+        self.iteration += 1
+        self.beta = self.optimal_beta_selection()