.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/examples_bbo/plot_black_box_optimization.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_examples_bbo_plot_black_box_optimization.py: Black-Box Optimization ====================== **Author(s)**: Romain Egele, Brett Eiffert. In this tutorial, we introduce you to the notion of `black-box optimization (Wikipedia) `_ (a.k.a., derivative-free optimization) with DeepHyper. Black-box optimization is a field of optimization research where an objective function :math:`f(x) = y \in \mathbb{R}` is optimized only based on input-output observations :math:`\{ (x_1,y_1), \ldots, (x_n, y_n) \}`. Let's start by installing DeepHyper! .. GENERATED FROM PYTHON SOURCE LINES 15-19 .. code-block:: bash %%bash pip install deephyper .. GENERATED FROM PYTHON SOURCE LINES 22-23 Then, we can import it and check the installed version: .. GENERATED FROM PYTHON SOURCE LINES 23-27 .. code-block:: Python import deephyper print(deephyper.__version__) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.10.2 .. GENERATED FROM PYTHON SOURCE LINES 28-41 Optimization Problem -------------------- The optimization problem is based on two components: 1. The black-box function that we want to optimize. 2. The search space or domain of input variables over which we want to optimize. Black-Box Function ~~~~~~~~~~~~~~~~~~ DeepHyper is developed to optimize black-box functions. Here, we define the function :math:`f(x) = - x ^ 2` that we want to maximise (the maximum being :math:`f(x=0) = 0` on :math:`I_x = [-10;10]`). The black-box function ``f`` takes as input a ``job`` that follows a dictionary interface from which we retrieve the variables of interest. .. GENERATED FROM PYTHON SOURCE LINES 43-46 .. code-block:: Python def f(job): return -job.parameters["x"] ** 2 .. GENERATED FROM PYTHON SOURCE LINES 47-51 Search Space of Input Variables ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this example, we have only one variable :math:`x` for the black-box functin :math:`f`. We empirically decide to optimize this variable $x$ on the interval :math:`I_x = [-10;10]`. To do so we use the :class:`deephyper.hpo.HpProblem` from DeepHyper and add a **real** hyperparameter by using a tuple of two floats. .. GENERATED FROM PYTHON SOURCE LINES 53-63 .. code-block:: Python from deephyper.hpo import HpProblem problem = HpProblem() # Define the variable you want to optimize problem.add_hyperparameter((-10.0, 10.0), "x") problem .. rst-class:: sphx-glr-script-out .. code-block:: none Configuration space object: Hyperparameters: x, Type: UniformFloat, Range: [-10.0, 10.0], Default: 0.0 .. GENERATED FROM PYTHON SOURCE LINES 64-73 Evaluator Interface ------------------- DeepHyper uses an API called :class:`deephyper.evaluator.Evaluator` to distribute the computation of black-box functions and adapt to different backends (e.g., threads, processes, MPI, Ray). An ``Evaluator`` object wraps the black-box function ``f`` that we want to optimize. Then a ``method`` parameter is used to select the backend and ``method_kwargs`` defines some available options of this backend. .. hint:: The ``method="thread"`` provides parallel computation only if the black-box is releasing the global interpretor lock (GIL). Therefore, if you want parallelism in Jupyter notebooks you should use the Ray evaluator (``method="ray"``) after installing Ray with ``pip install ray``. It is possible to define callbacks to extend the behaviour of ``Evaluator`` each time a function-evaluation is launched or completed. In this example we use the :class:`deephyper.evaluator.callback.TqdmCallback` to follow the completed evaluations and the evolution of the objective with a progress-bar. .. GENERATED FROM PYTHON SOURCE LINES 73-90 .. code-block:: Python from deephyper.evaluator import Evaluator from deephyper.evaluator.callback import TqdmCallback # define the evaluator to distribute the computation evaluator = Evaluator.create( f, method="thread", method_kwargs={ "num_workers": 4, "callbacks": [TqdmCallback()] }, ) print(f"Evaluator has {evaluator.num_workers} available worker{'' if evaluator.num_workers == 1 else 's'}") .. rst-class:: sphx-glr-script-out .. code-block:: none Evaluator has 4 available workers .. GENERATED FROM PYTHON SOURCE LINES 91-95 Search Algorithm ---------------- The next step is to define the search algorithm that we want to use. Here, we choose :class:`deephyper.hpo.CBO` (Centralized Bayesian Optimization) which is a sampling based Bayesian optimization strategy. This algorithm has the advantage of being asynchronous thanks to a constant liar strategy which is crutial to keep a good utilization of the resources when the number of available workers increases. .. GENERATED FROM PYTHON SOURCE LINES 95-106 .. code-block:: Python from deephyper.hpo import CBO # define your search def create_search(): search = CBO( problem, acq_optimizer="ga", ) return search .. GENERATED FROM PYTHON SOURCE LINES 107-117 Then, to execute the search we provide two interfaces. Ask and Tell Interface ~~~~~~~~~~~~~~~~~~~~~~ The first interface is the classic ``configurations = search.ask(...)`` and ``search.tell(configurations_with_objective)``. In this case, you need to manage the computation of objectives yourself. This interface is more flexible. However, asynchronous parallel evaluations are not managed for you. Here is an example: .. GENERATED FROM PYTHON SOURCE LINES 117-126 .. code-block:: Python search = create_search() max_evals = 100 for i in range(max_evals): config = search.ask(1)[0] y = -config["x"] ** 2 print(f"[{i=:03d}] >>> f(x={config['x']:.3f}) = {y:.3f}") search.tell([(config, y)]) .. rst-class:: sphx-glr-script-out .. code-block:: none [i=000] >>> f(x=-0.150) = -0.022 [i=001] >>> f(x=-9.819) = -96.421 [i=002] >>> f(x=3.473) = -12.065 [i=003] >>> f(x=-1.518) = -2.305 [i=004] >>> f(x=-3.703) = -13.709 [i=005] >>> f(x=-0.002) = -0.000 [i=006] >>> f(x=-0.501) = -0.251 [i=007] >>> f(x=-0.878) = -0.771 [i=008] >>> f(x=0.194) = -0.038 [i=009] >>> f(x=-0.610) = -0.372 [i=010] >>> f(x=-0.814) = -0.662 [i=011] >>> f(x=-0.195) = -0.038 [i=012] >>> f(x=-0.089) = -0.008 [i=013] >>> f(x=-0.433) = -0.188 [i=014] >>> f(x=1.639) = -2.685 [i=015] >>> f(x=-1.606) = -2.580 [i=016] >>> f(x=0.245) = -0.060 [i=017] >>> f(x=-0.028) = -0.001 [i=018] >>> f(x=-0.062) = -0.004 [i=019] >>> f(x=0.003) = -0.000 [i=020] >>> f(x=0.082) = -0.007 [i=021] >>> f(x=-0.060) = -0.004 [i=022] >>> f(x=0.091) = -0.008 [i=023] >>> f(x=0.097) = -0.009 [i=024] >>> f(x=0.394) = -0.155 [i=025] >>> f(x=0.668) = -0.446 [i=026] >>> f(x=0.085) = -0.007 [i=027] >>> f(x=0.002) = -0.000 [i=028] >>> f(x=-0.085) = -0.007 [i=029] >>> f(x=-0.099) = -0.010 [i=030] >>> f(x=-0.064) = -0.004 [i=031] >>> f(x=-0.050) = -0.003 [i=032] >>> f(x=-0.056) = -0.003 [i=033] >>> f(x=-0.017) = -0.000 [i=034] >>> f(x=0.443) = -0.196 [i=035] >>> f(x=-0.216) = -0.046 [i=036] >>> f(x=0.187) = -0.035 [i=037] >>> f(x=-0.080) = -0.006 [i=038] >>> f(x=-0.042) = -0.002 [i=039] >>> f(x=0.084) = -0.007 [i=040] >>> f(x=-0.010) = -0.000 [i=041] >>> f(x=0.021) = -0.000 [i=042] >>> f(x=0.021) = -0.000 [i=043] >>> f(x=0.022) = -0.000 [i=044] >>> f(x=-0.305) = -0.093 [i=045] >>> f(x=0.262) = -0.069 [i=046] >>> f(x=-0.007) = -0.000 [i=047] >>> f(x=0.023) = -0.001 [i=048] >>> f(x=0.031) = -0.001 [i=049] >>> f(x=0.030) = -0.001 [i=050] >>> f(x=0.026) = -0.001 [i=051] >>> f(x=0.022) = -0.000 [i=052] >>> f(x=0.016) = -0.000 [i=053] >>> f(x=0.020) = -0.000 [i=054] >>> f(x=0.287) = -0.082 [i=055] >>> f(x=-0.123) = -0.015 [i=056] >>> f(x=0.102) = -0.010 [i=057] >>> f(x=0.015) = -0.000 [i=058] >>> f(x=-0.008) = -0.000 [i=059] >>> f(x=-0.007) = -0.000 [i=060] >>> f(x=-0.006) = -0.000 [i=061] >>> f(x=-0.019) = -0.000 [i=062] >>> f(x=-0.013) = -0.000 [i=063] >>> f(x=-0.008) = -0.000 [i=064] >>> f(x=0.132) = -0.017 [i=065] >>> f(x=0.016) = -0.000 [i=066] >>> f(x=0.016) = -0.000 [i=067] >>> f(x=0.013) = -0.000 [i=068] >>> f(x=0.015) = -0.000 [i=069] >>> f(x=-0.011) = -0.000 [i=070] >>> f(x=-0.006) = -0.000 [i=071] >>> f(x=0.008) = -0.000 [i=072] >>> f(x=0.012) = -0.000 [i=073] >>> f(x=0.014) = -0.000 [i=074] >>> f(x=0.033) = -0.001 [i=075] >>> f(x=0.041) = -0.002 [i=076] >>> f(x=0.004) = -0.000 [i=077] >>> f(x=0.010) = -0.000 [i=078] >>> f(x=0.007) = -0.000 [i=079] >>> f(x=0.009) = -0.000 [i=080] >>> f(x=0.007) = -0.000 [i=081] >>> f(x=0.005) = -0.000 [i=082] >>> f(x=0.004) = -0.000 [i=083] >>> f(x=0.005) = -0.000 [i=084] >>> f(x=0.050) = -0.002 [i=085] >>> f(x=-0.010) = -0.000 [i=086] >>> f(x=0.011) = -0.000 [i=087] >>> f(x=0.000) = -0.000 [i=088] >>> f(x=-0.010) = -0.000 [i=089] >>> f(x=-0.011) = -0.000 [i=090] >>> f(x=-0.010) = -0.000 [i=091] >>> f(x=-0.009) = -0.000 [i=092] >>> f(x=0.003) = -0.000 [i=093] >>> f(x=-0.008) = -0.000 [i=094] >>> f(x=0.063) = -0.004 [i=095] >>> f(x=-0.005) = -0.000 [i=096] >>> f(x=-0.007) = -0.000 [i=097] >>> f(x=0.003) = -0.000 [i=098] >>> f(x=-0.001) = -0.000 [i=099] >>> f(x=-0.001) = -0.000 .. GENERATED FROM PYTHON SOURCE LINES 127-132 Search Interface ~~~~~~~~~~~~~~~~ The second interface is ``results = search.search(evaluator, ...)`` that is binded to the ``evaluator`` and manages the loop for asynchronous parallel evaluations for you. We can execute the search for a given number of iterations by using the ``search.search(evaluator, max_evals=...)``. It is also possible to use the ``timeout`` parameter if one needs a specific time budget (e.g., restricted computational time in machine learning competitions, allocation time in HPC). .. GENERATED FROM PYTHON SOURCE LINES 132-136 .. code-block:: Python search = create_search() results = search.search(evaluator, max_evals) .. rst-class:: sphx-glr-script-out .. code-block:: none 0%| | 0/100 [00:00
p:x objective job_id job_status m:timestamp_submit m:timestamp_gather
0 0.714013 -0.509815 0 DONE 16.055601 16.056108
1 -7.299946 -53.289215 2 DONE 16.055627 16.062735
2 2.997893 -8.987361 1 DONE 16.055620 16.062853
3 8.294617 -68.800670 3 DONE 16.055632 16.062946
4 5.378610 -28.929448 4 DONE 16.936808 16.937233
... ... ... ... ... ... ...
98 -0.260893 -0.068065 96 DONE 35.183628 35.345498
99 -0.330581 -0.109284 99 DONE 35.345077 35.986678
100 -0.267424 -0.071516 102 DONE 35.986451 36.149026
101 -0.047429 -0.002249 100 DONE 35.986431 36.149059
102 -0.062054 -0.003851 101 DONE 35.986446 36.149077

103 rows × 6 columns



.. GENERATED FROM PYTHON SOURCE LINES 150-151 To get the parameters at the observed maximum value we can use the :func:`deephyper.analysis.hpo.parameters_at_max`: .. GENERATED FROM PYTHON SOURCE LINES 151-160 .. code-block:: Python from deephyper.analysis.hpo import parameters_at_max parameters, objective = parameters_at_max(results) print("\nOptimum values") print("x:", parameters["x"]) print("objective:", objective) .. rst-class:: sphx-glr-script-out .. code-block:: none Optimum values x: -0.00036876827022958025 objective: -1.3599003712811672e-07 .. GENERATED FROM PYTHON SOURCE LINES 161-162 We can also plot the evolution of the objective to verify that we converge correctly toward :math:`0`. .. GENERATED FROM PYTHON SOURCE LINES 162-174 .. code-block:: Python import matplotlib.pyplot as plt from deephyper.analysis.hpo import plot_search_trajectory_single_objective_hpo WIDTH_PLOTS = 8 HEIGHT_PLOTS = WIDTH_PLOTS / 1.618 fig, ax = plt.subplots(figsize=(WIDTH_PLOTS, HEIGHT_PLOTS)) plot_search_trajectory_single_objective_hpo(results, mode="min", ax=ax) _ = plt.title("Search Trajectory") _ = plt.yscale("log") .. image-sg:: /examples/examples_bbo/images/sphx_glr_plot_black_box_optimization_001.png :alt: Search Trajectory :srcset: /examples/examples_bbo/images/sphx_glr_plot_black_box_optimization_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 37.458 seconds) .. _sphx_glr_download_examples_examples_bbo_plot_black_box_optimization.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_black_box_optimization.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_black_box_optimization.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_black_box_optimization.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_