.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_exploration-vs-exploitation.py: =========================== Exploration vs exploitation =========================== Sigurd Carlen, September 2019. Reformatted by Holger Nahrstaedt 2020 .. currentmodule:: skopt We can control how much the acqusition function favors exploration and exploitation by tweaking the two parameters kappa and xi. Higher values means more exploration and less exploitation and vice versa with low values. kappa is only used if acq_func is set to "LCB". xi is used when acq_func is "EI" or "PI". By default the acqusition function is set to "gp_hedge" which chooses the best of these three. Therefore I recommend not using gp_hedge when tweaking exploration/exploitation, but instead choosing "LCB", "EI" or "PI". The way to pass kappa and xi to the optimizer is to use the named argument "acq_func_kwargs". This is a dict of extra arguments for the aqcuisition function. If you want opt.ask() to give a new acquisition value immediately after tweaking kappa or xi call opt.update_next(). This ensures that the next value is updated with the new acquisition parameters. This example uses :class:`plots.plot_gaussian_process` which is available since version 0.8. .. code-block:: default print(__doc__) import numpy as np np.random.seed(1234) import matplotlib.pyplot as plt from skopt.learning import ExtraTreesRegressor from skopt import Optimizer from skopt.plots import plot_gaussian_process Toy example ----------- First we define our objective like in the ask-and-tell example notebook and define a plotting function. We do however only use on initial random point. All points after the first one is therefore chosen by the acquisition function. .. code-block:: default noise_level = 0.1 # Our 1D toy problem, this is the function we are trying to # minimize def objective(x, noise_level=noise_level): return np.sin(5 * x[0]) * (1 - np.tanh(x[0] ** 2)) +\ np.random.randn() * noise_level def objective_wo_noise(x): return objective(x, noise_level=0) .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_optimizer="sampling") Plotting parameters .. code-block:: default plot_args = {"objective": objective_wo_noise, "noise_level": noise_level, "show_legend": True, "show_title": True, "show_next_point": False, "show_acq_func": True} We run a an optimization loop with standard settings .. code-block:: default for i in range(30): next_x = opt.ask() f_val = objective(next_x) opt.tell(next_x, f_val) # The same output could be created with opt.run(objective, n_iter=30) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_001.png :alt: x* = -0.2913, f(x*) = -1.0409 :class: sphx-glr-single-img We see that some minima is found and "exploited" Now lets try to set kappa and xi using'to other values and pass it to the optimizer: .. code-block:: default acq_func_kwargs = {"xi": 10000, "kappa": 10000} .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_002.png :alt: x* = -0.3083, f(x*) = -0.7990 :class: sphx-glr-single-img We see that the points are more random now. This works both for kappa when using acq_func="LCB": .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="LCB", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_003.png :alt: x* = -0.1829, f(x*) = -0.8271 :class: sphx-glr-single-img And for xi when using acq_func="EI": or acq_func="PI": .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="PI", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_004.png :alt: x* = -0.3877, f(x*) = -0.8487 :class: sphx-glr-single-img We can also favor exploitaton: .. code-block:: default acq_func_kwargs = {"xi": 0.000001, "kappa": 0.001} .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="LCB", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_005.png :alt: x* = -0.4020, f(x*) = -0.9123 :class: sphx-glr-single-img .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="EI", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_006.png :alt: x* = 0.8760, f(x*) = -0.4154 :class: sphx-glr-single-img .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="PI", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_007.png :alt: x* = -0.2782, f(x*) = -1.1051 :class: sphx-glr-single-img Note that negative values does not work with the "PI"-acquisition function but works with "EI": .. code-block:: default acq_func_kwargs = {"xi": -1000000000000} .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="PI", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_008.png :alt: x* = 0.8093, f(x*) = -0.4621 :class: sphx-glr-single-img .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="EI", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_009.png :alt: x* = 0.8341, f(x*) = -0.4331 :class: sphx-glr-single-img Changing kappa and xi on the go ------------------------------- If we want to change kappa or ki at any point during our optimization process we just replace opt.acq_func_kwargs. Remember to call `opt.update_next()` after the change, in order for next point to be recalculated. .. code-block:: default acq_func_kwargs = {"kappa": 0} .. code-block:: default opt = Optimizer([(-2.0, 2.0)], "GP", n_initial_points=3, acq_func="LCB", acq_optimizer="sampling", acq_func_kwargs=acq_func_kwargs) .. code-block:: default opt.acq_func_kwargs .. rst-class:: sphx-glr-script-out Out: .. code-block:: none {'kappa': 0} .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_010.png :alt: x* = -0.2982, f(x*) = -1.0610 :class: sphx-glr-single-img .. code-block:: default acq_func_kwargs = {"kappa": 100000} .. code-block:: default opt.acq_func_kwargs = acq_func_kwargs opt.update_next() .. code-block:: default opt.run(objective, n_iter=20) _ = plot_gaussian_process(opt.get_result(), **plot_args) .. image:: /auto_examples/images/sphx_glr_exploration-vs-exploitation_011.png :alt: x* = -0.2982, f(x*) = -1.0610 :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 29.821 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_auto_examples_exploration-vs-exploitation.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: /../../miniconda/envs/testenv/lib/python3.8/site-packages/sphinx_gallery/_static/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-optimize/scikit-optimize/master?urlpath=lab/tree/notebooks/auto_examples/exploration-vs-exploitation.ipynb :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: exploration-vs-exploitation.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: exploration-vs-exploitation.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_