.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/examples_bbo/plot_constrained_black_box_optimization_chained_sampler.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_constrained_black_box_optimization_chained_sampler.py: Constrained Black-Box Optimization with Custom Chained Sampler ============================================================== **Author(s)**: Romain Egele. This tutorial demonstrates how to solve *constrained* `black-box optimization `_ using **DeepHyper**, focusing on how to encode structural constraints directly in the **sampling strategy** of the search algorithm. Black-box optimization aims to optimize an unknown function :math:`f(x) = y \in \mathbb{R}` using only input–output evaluations :math:`\{(x_1, y_1), \ldots, (x_n, y_n)\}`. No analytical gradients or structural properties of :math:`f` are required. In *constrained* settings, the search is further restricted to parameters that satisfy one or more feasibility rules. Constraints can significantly reshape the search space and modify the behavior of the optimizer. Problem Setting --------------- In this example, we consider a *discrete*, *ordered* search space of dimension :math:`N`. Each variable :math:`x_i` must satisfy the **monotonicity constraint** .. math:: x_0 < x_1 < \cdots < x_{N-1}. Each :math:`x_i` is bounded between :math:`i` and :math:`m - N + i`. This could tipically represent the layer indexes to drop in Depth pruning of Large language models. The objective is to **maximize** the sum .. math:: f(x) = \sum_{i=0}^{N-1} x_i. Since the optimal strategy is to push every variable as high as possible while respecting monotonicity, the theoretical optimum is: .. math:: \sum_{i=0}^{N-1} (m - i). DeepHyper offers several ways to incorporate constraints: #. **Custom chained sampler** *(this tutorial)*: constraints are enforced directly when generating new candidate points. #. **Rejection sampling**: see :ref:`Constrained Black-Box Optimization with Rejection Sampling `. #. **Learning to avoid failures** (CBO auto-handles failed evaluations): see this tutorial and also :ref:`Learn to Avoid Failures with Bayesian Optimization `. #. **Multi-objective approach** where the constraint becomes an additional objective (tutorial forthcoming). .. GENERATED FROM PYTHON SOURCE LINES 61-75 .. code-block:: Python import matplotlib.pyplot as plt import matplotlib.cm as cm import matplotlib.colors as colors import numpy as np import pandas as pd from deephyper.analysis.hpo import ( plot_search_trajectory_single_objective_hpo, parameters_at_max, filter_failed_objectives, ) from deephyper.hpo import HpProblem, CBO .. GENERATED FROM PYTHON SOURCE LINES 76-89 Custom Chained Sampler ---------------------- Because every :math:`x_i` must be strictly larger than :math:`x_{i-1}`, the usual independent sampling over each variable would frequently violate the constraint. Instead, we implement a *chained* sampler: each :math:`x_k` is sampled conditionally so that enough "room" remains for future variables. This ensures that: - all generated samples satisfy :math:`x_i < x_{i+1}` by construction; - the sampler focuses on the feasible region, avoiding wasted evaluations. .. GENERATED FROM PYTHON SOURCE LINES 89-118 .. code-block:: Python n = 10 m = 32 print("optimum:", sum([m - i - 1 for i in range(n)])) pb = HpProblem() for i in range(n): pb.add((i, m - n + i - 1), f"x{i}") def sampling_fn(size: int) -> list[dict]: def sample_chain(): # Chain the sampling vals = [] lo = 0 for k in range(n): low = max(k, lo + 1 if k > 0 else 0) high = m - n + k v = np.random.randint(low, high - (n - 1 - k)) # keep room for future vars vals.append(v) lo = v return {k: v for k, v in zip(pb.hyperparameter_names, vals)} return [sample_chain() for _ in range(size)] pb.set_sampling_fn(sampling_fn) .. rst-class:: sphx-glr-script-out .. code-block:: none optimum: 265 .. GENERATED FROM PYTHON SOURCE LINES 119-128 Constraint Function ------------------- Although the sampler already generates feasible points, we explicitly define a ``constraint_fn``. This allows DeepHyper to properly handle *failed* trials (e.g., from manually constructed parameter sets or mutation-based acquisition optimizers). Not only that, this will help report non-feasible points using ``"F_constraint"`` in the objective function so that CBO learns to avoid them. .. GENERATED FROM PYTHON SOURCE LINES 128-150 .. code-block:: Python def constraint_fn(df: pd.DataFrame) -> pd.Series: accept = pd.Series(np.ones((len(df)), dtype=bool)) for i in range(n - 1): accept = accept & (df[f"x{i}"] < df[f"x{i + 1}"]) return accept pb.set_constraint_fn(constraint_fn) def f(job): """Objective function: maximize sum(x_i).""" df = pd.DataFrame([job.parameters]) accept = constraint_fn(df) if all(accept): return sum(job.parameters.values()) else: return "F_constraint" .. GENERATED FROM PYTHON SOURCE LINES 151-164 Bayesian Optimization with Mixed-GA Acquisition Optimization ------------------------------------------------------------ We run a **Centralized Bayesian Optimization (CBO)** search using: - Ensemble of Trees surrogate model (``"ET"``). - A **mixed genetic algorithm** (``"mixedga"``) to optimize the acquisition function. - A **periodically decaying scheduler** on the exploration parameter ``kappa``. This setup is well suited for discrete, irregularly constrained spaces. The search runs for ``max_evals=300`` iterations. .. GENERATED FROM PYTHON SOURCE LINES 164-188 .. code-block:: Python search = CBO( pb, surrogate_model="ET", surrogate_model_kwargs={"max_features": "sqrt"}, acq_optimizer="mixedga", acq_optimizer_kwargs={ "n_points": 1_000, "acq_optimizer_freq": 2, "filter_failures": "mean", }, acq_func_kwargs={ # Exploration/Exploitation mechanism "kappa": 10.0, "scheduler": { "type": "periodic-exp-decay", "period": 20, "kappa_final": 0.1, }, }, verbose=1, ) results = search.search(f, max_evals=300) .. rst-class:: sphx-glr-script-out .. code-block:: none 0%| | 0/300 [00:00
p:x0 p:x1 p:x2 p:x3 p:x4 p:x5 p:x6 p:x7 p:x8 p:x9 objective job_id job_status m:timestamp_submit m:timestamp_gather
0 6 12 15 17 19 20 24 25 26 27 191.0 0 DONE 0.015556 0.016203
1 1 7 13 16 19 21 23 24 27 30 181.0 1 DONE 0.035443 0.036249
2 10 14 15 17 18 20 24 25 27 28 198.0 2 DONE 0.049745 0.050325
3 11 13 14 16 18 19 24 26 28 29 198.0 3 DONE 0.064089 0.064661
4 1 14 16 18 20 22 23 25 26 27 192.0 4 DONE 0.077750 0.078269
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
295 19 21 23 24 25 26 27 28 29 30 252.0 295 DONE 110.451081 110.451661
296 12 14 16 17 20 22 24 26 28 30 209.0 296 DONE 110.473861 110.474404
297 20 21 23 24 25 26 27 28 29 30 253.0 297 DONE 111.577984 111.578579
298 12 14 16 18 19 22 24 26 27 29 207.0 298 DONE 111.600968 111.601481
299 20 21 23 24 25 26 27 28 29 30 253.0 299 DONE 112.907730 112.908327

300 rows × 15 columns



.. GENERATED FROM PYTHON SOURCE LINES 192-196 Extracting the Best Parameters ------------------------------ To recover the parameters corresponding to the best observed objective value, we can use :func:`deephyper.analysis.hpo.parameters_at_max`. .. GENERATED FROM PYTHON SOURCE LINES 196-203 .. code-block:: Python parameters, objective = parameters_at_max(results) print("\nOptimum values") for i in range(n): print(f"x{i}: {parameters[f'x{i}']:.3f}") print("objective:", objective) .. rst-class:: sphx-glr-script-out .. code-block:: none Optimum values x0: 20.000 x1: 21.000 x2: 23.000 x3: 24.000 x4: 25.000 x5: 26.000 x6: 27.000 x7: 28.000 x8: 29.000 x9: 30.000 objective: 253.0 .. GENERATED FROM PYTHON SOURCE LINES 204-217 Visualization --------------- We conclude with: - a **search trajectomakery plot** showing the best objective value over time, where the periodic exploration schedule is clearly visible; - a **feasible-space evaluation plot** showing all sampled curves :math:`i \mapsto x_i` (each curve is one evaluation), colored by objective value. These visualizations confirm that the optimizer progressively learns the structure of the monotonic constraint and approaches the theoretical optimum. .. GENERATED FROM PYTHON SOURCE LINES 217-225 .. code-block:: Python 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="max", ax=ax) _ = plt.title("Search Trajectory") .. image-sg:: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_chained_sampler_001.png :alt: Search Trajectory :srcset: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_chained_sampler_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 226-230 Visualizing the Feasible Region and Evaluations ----------------------------------------------- We now plot all evaluated points in the (x, y) plane, color-coded by objective value, along with the constraint boundary ``x + y = 10``. .. GENERATED FROM PYTHON SOURCE LINES 230-266 .. code-block:: Python results, _ = filter_failed_objectives(results) p_columns = [col for col in results.columns if col.startswith("p:")] # Create a normalizer over the objective range obj_vals = results["objective"] norm = colors.Normalize(vmin=obj_vals.min(), vmax=obj_vals.max()) # Choose a colormap (viridis is a good default) cmap = plt.get_cmap("viridis") fig, ax = plt.subplots(figsize=(WIDTH_PLOTS, HEIGHT_PLOTS)) for i, row in results.iterrows(): x_values = row[p_columns].values y_values = np.arange(n) obj_value = row["objective"] color = cmap(norm(obj_value)) # map objective → color ax.plot(x_values, y_values, color=color, alpha=0.9) # Optionally add a colorbar sm = cm.ScalarMappable(norm=norm, cmap=cmap) cbar = fig.colorbar(sm, ax=ax) cbar.set_label("Objective value") ax.grid() ax.set_ylim(0, n - 1) ax.set_xlim(0, m) ax.set_ylabel(r"$i$") ax.set_xlabel(r"$x_i$") ax.set_yticks(list(range(n)), [str(i) for i in range(n)]) ax.set_xticks(list(range(0, m, 2)), [str(i) for i in range(0, m, 2)]) .. image-sg:: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_chained_sampler_002.png :alt: plot constrained black box optimization chained sampler :srcset: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_chained_sampler_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none [, , , , , , , , , , , , , , , ] .. rst-class:: sphx-glr-timing **Total running time of the script:** (1 minutes 54.009 seconds) .. _sphx_glr_download_examples_examples_bbo_plot_constrained_black_box_optimization_chained_sampler.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_constrained_black_box_optimization_chained_sampler.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_constrained_black_box_optimization_chained_sampler.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_constrained_black_box_optimization_chained_sampler.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_