.. 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_noisy.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_noisy.py: Noisy Black-Box Optimization ============================ **Author(s)**: Romain Egele. In this tutorial, we show you how to manage **noisy** `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 22-52 Optimization Problem -------------------- The optimization problem consists of two components: 1. The *black-box function* that we aim to optimize. 2. The *search space* (or domain) of input variables over which the optimization is performed. Black-Box Function ~~~~~~~~~~~~~~~~~~ In DeepHyper, black-box optimization is performed on user-defined functions that can be noisy or stochastic. Below, we define a noisy black-box function `f` that depends on a single variable :math:`x` in the domain :math:`I_x = [-10, 10]`. The noisy black-box function is defined as: .. math:: f(x) = \text{Binomial}(n=1, p(x)) where the probability of success is: .. math:: p(x) = \frac{100 - x^2}{100}. This means that for each evaluation, `f(x)` returns a random binary value (0 or 1) with probability `p(x)` of success. The maximum expected value of :math:`f(x)` is obtained at :math:`x = 0`, where :math:`p(0) = 1`. The function `f` takes as input a `job`, which behaves like a dictionary. The variable of interest `x` is accessed via `job.parameters["x"]`. .. GENERATED FROM PYTHON SOURCE LINES 54-62 .. code-block:: Python import numpy as np def f(job): p = (100 - job.parameters["x"] ** 2) / 100 obs = np.random.binomial(n=1, p=p) return obs .. GENERATED FROM PYTHON SOURCE LINES 63-67 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 69-79 .. 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 80-89 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 89-106 .. 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": 1, "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 1 available worker .. GENERATED FROM PYTHON SOURCE LINES 107-117 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 which is crutial to keep a good utilization of the resources when the number of available workers increases. We also choose, how to optimize the acquisition function of the Bayesian optimization with ``"ga"`` (i.e., continuous Genetic Algorithm). Then, we setup a solution selection method. Here we use :class:`deephyper.hpo.ArgMaxEstSelection`, that will select the optimum based on the estimated maximum of a surrogate model. The ``model_grid_search=True`` activates the auto-tuning of the surrogate model every 100 observations by default. The ``noisy_objective=True`` sets the default configuration of the surrogate model for a noisy objective. .. GENERATED FROM PYTHON SOURCE LINES 117-137 .. code-block:: Python from deephyper.hpo import CBO, ArgMaxEstSelection def create_search(): search = CBO( problem, acq_optimizer="ga", solution_selection=ArgMaxEstSelection( problem, model_grid_search=True, noisy_objective=True, ), ) return search max_evals = 300 search = create_search() results = search.search(evaluator, max_evals) .. rst-class:: sphx-glr-script-out .. code-block:: none Results file already exists, it will be renamed to /Users/rp5/Documents/DeepHyper/deephyper/examples/examples_bbo/results_20251021-154659.csv 0%| | 0/300 [00:00
p:x objective job_id job_status m:timestamp_submit m:timestamp_gather sol.p:x sol.objective sol.objective_std_al sol.objective_std_ep
0 -5.897543 1.0 0 DONE 0.008010 0.008471 3.787579 1.0000 0.000000 0.000000
1 1.173746 1.0 1 DONE 0.601424 0.601710 4.478960 1.0000 0.000000 0.000000
2 -8.123233 0.0 2 DONE 1.170570 1.170761 -3.484530 0.6400 0.382971 0.289367
3 -5.765876 0.0 3 DONE 1.917559 1.917737 4.345440 0.4575 0.425000 0.259940
4 -0.429996 1.0 4 DONE 2.610857 2.611031 -8.594116 0.6120 0.438178 0.213204
... ... ... ... ... ... ... ... ... ... ...
295 1.884849 1.0 295 DONE 233.669751 233.669944 0.867834 1.0000 0.000000 0.000000
296 -5.175182 1.0 296 DONE 234.377051 234.377236 0.194228 1.0000 0.000000 0.000000
297 3.121228 1.0 297 DONE 235.143700 235.143892 -0.569485 1.0000 0.000000 0.000000
298 -8.950916 0.0 298 DONE 235.844466 235.844659 1.215950 1.0000 0.000000 0.000000
299 4.389502 0.0 299 DONE 236.546905 236.547096 0.284153 1.0000 0.000000 0.000000

300 rows × 10 columns



.. GENERATED FROM PYTHON SOURCE LINES 156-159 To get the parameters at the observed maximum value we can use the :func:`deephyper.analysis.hpo.parameters_at_max`: We make sure to select the right column and prefix for parameters. Also, we prefer to select the solution amoung the ``n_last=20`` rows to avoid selecting noisy observations at the beginning. .. GENERATED FROM PYTHON SOURCE LINES 159-167 .. code-block:: Python from deephyper.analysis.hpo import parameters_at_max parameters, objective = parameters_at_max(results, column="sol.objective", prefix="sol.p:", n_last=20) print("\nEstimated Optimum values") print("x:", parameters["x"]) print("objective:", objective) .. rst-class:: sphx-glr-script-out .. code-block:: none Estimated Optimum values x: 0.28415316302867666 objective: 1.0 .. GENERATED FROM PYTHON SOURCE LINES 168-169 We can also plot the evolution of the estimated solution value of :math:`x` to verify that we converge correctly toward :math:`x=0`. .. GENERATED FROM PYTHON SOURCE LINES 169-181 .. 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, column="sol.p:x", mode="max", ax=ax) _ = ax.set_ylabel(r"Estimated solution $x$") _ = ax.set_ylim(-10, 10) _ = plt.title("Search Trajectory") .. image-sg:: /examples/examples_bbo/images/sphx_glr_plot_black_box_optimization_noisy_001.png :alt: Search Trajectory :srcset: /examples/examples_bbo/images/sphx_glr_plot_black_box_optimization_noisy_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (4 minutes 13.660 seconds) .. _sphx_glr_download_examples_examples_bbo_plot_black_box_optimization_noisy.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_noisy.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_black_box_optimization_noisy.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_black_box_optimization_noisy.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_