.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "getting_started/auto_examples/plot_HCT_Himmelblau.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_getting_started_auto_examples_plot_HCT_Himmelblau.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_getting_started_auto_examples_plot_HCT_Himmelblau.py:


2-D Example
===================
In this example, we run the HCT algorithm on the normalized Himmelblau objective. First, import all the functions needed

.. GENERATED FROM PYTHON SOURCE LINES 7-19

.. code-block:: default


    from PyXAB.synthetic_obj.Himmelblau import Himmelblau_Normalized        # the objective
    from PyXAB.algos.HCT import HCT                                       # the algorithm
    from PyXAB.partition.BinaryPartition import BinaryPartition             # the partition

    # the other useful packages/functions
    import numpy as np
    from PyXAB.utils.plot import plot_regret











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Define the number of rounds, the target, the domain, the partition, and the algorithm for the learning process

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.. code-block:: default

    T = 1000                                                    # the number of rounds is 1000
    target = Himmelblau_Normalized()                            # the objective to optimize is the normalized Himmelblau
    domain = [[-5, 5], [-5, 5]]                                 # the domain is [[-5, 5], [-5, 5]]
    partition = BinaryPartition                                 # the partition chosen is BinaryPartition
    algo = HCT(domain=domain, partition=partition)              # the algorithm is HCT








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To plot the regret, we can initialize the cumulative regret and the cumulative regret list

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.. code-block:: default


    cumulative_regret = 0
    cumulative_regret_list = []









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In each iteration of the learning process, the algorithm calls the ``pull(t)`` function to obtain a point, and then
the reward for the point is returned to the algorithm by calling ``receive_reward(t, reward)``.
For a stochastic learning process, uniform noise is added to the reward.

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.. code-block:: default


    for t in range(1, T+1):

        point = algo.pull(t)
        reward = target.f(point) + np.random.uniform(-0.1, 0.1)         # uniform noise
        algo.receive_reward(t, reward)

        # the following lines are for the regret
        inst_regret = target.fmax - target.f(point)
        cumulative_regret += inst_regret
        cumulative_regret_list.append(cumulative_regret)


    # plot the regret
    plot_regret(np.array(cumulative_regret_list), name='HCT')






.. image-sg:: /getting_started/auto_examples/images/sphx_glr_plot_HCT_Himmelblau_001.png
   :alt: plot HCT Himmelblau
   :srcset: /getting_started/auto_examples/images/sphx_glr_plot_HCT_Himmelblau_001.png
   :class: sphx-glr-single-img





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The following lines of code are only for creating thumbnails and do not need to be used

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.. code-block:: default


    # sphinx_gallery_thumbnail_number = 2
    import matplotlib.pyplot as plt
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')

    x = np.linspace(domain[0][0], domain[0][1], 1000)
    y = np.linspace(domain[0][0], domain[0][1], 1000)
    xx, yy = np.meshgrid(x, y)
    z = (- (xx ** 2 + yy - 11) ** 2 - (xx + yy ** 2 - 7) ** 2) / 890
    ax.plot_surface(xx, yy, z, alpha=0.9)
    fig.subplots_adjust(left=0.1, right=0.9, top=0.9, bottom=0.1)





.. image-sg:: /getting_started/auto_examples/images/sphx_glr_plot_HCT_Himmelblau_002.png
   :alt: plot HCT Himmelblau
   :srcset: /getting_started/auto_examples/images/sphx_glr_plot_HCT_Himmelblau_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.884 seconds)


.. _sphx_glr_download_getting_started_auto_examples_plot_HCT_Himmelblau.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example




    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_HCT_Himmelblau.py <plot_HCT_Himmelblau.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_HCT_Himmelblau.ipynb <plot_HCT_Himmelblau.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_