hoptimal

CI C++20 Python 3.9+ License: MIT

A from-scratch C++ Gaussian-Process Bayesian optimizer with Python bindings; competitive with Optuna and scikit-optimize on sample efficiency.

hoptimal implements Bayesian optimization for ML model hyperparameters (a Gaussian-Process surrogate + acquisition functions) in modern C++20, exposed to Python through pybind11.

Benchmark

Median regret vs trial number on 8 standard optimization test functions, 8 seeds each: hoptimal against Optuna and scikit-optimize:

regret curves

Across the 8 functions, hoptimal's GP wins 3 outright (Hartmann-6, Ackley, Rosenbrock) and places a close 2nd on the rest. It beats every Optuna sampler on 6 of 8 — losing only levy/rastrigin to CMA-ES — and is edged on the two smooth low-dimensional functions by scikit-optimize (by decimals). It is strongest on the higher-dimensional problems.

Function hoptimal (best) Optuna (best) scikit-optimize
branin 0.0013 0.70 0.0011
hartmann3 0.0004 0.15 0.0002
hartmann6 0.044 1.06 0.14
ackley5 2.21 3.30 2.88
rosenbrock4 4.37 10.4 11.9
levy5 2.37 2.07 3.55
rastrigin5 29.5 27.7 33.6
styblinski5 47.9 55.5 26.5

Reproduce: python benchmarks/python/competitors/bench_competitors.py && python benchmarks/python/visualize.py

Against Optuna's BoTorch-backed GP sampler specifically — the toughest GP-vs-GP comparison — hoptimal goes 4–4 on final quality, winning the harder higher-dimensional and multimodal functions (hartmann6, rosenbrock, rastrigin, styblinski). Reproduce (reports how many trials hoptimal saves to match Optuna): python benchmarks/python/bench_vs_optuna.py --optuna-sampler gp --save && python benchmarks/python/visualize_vs_optuna.py

Installation

pip install hoptimal

Prebuilt wheels are published for Linux, macOS (Intel + Apple Silicon), and Windows on CPython 3.9–3.13, so no C++ toolchain is required.

The ML-framework integrations pull in their own dependencies and are installed via extras:

pip install hoptimal[sklearn]     # scikit-learn
pip install hoptimal[xgboost]     # XGBoost
pip install hoptimal[lightgbm]    # LightGBM
pip install hoptimal[catboost]    # CatBoost
pip install hoptimal[torch]       # PyTorch
pip install hoptimal[jax]         # JAX + Flax
pip install hoptimal[tensorflow]  # TensorFlow / Keras
pip install hoptimal[viz]         # matplotlib plots + pandas + importances

Quickstart

import hoptimal

study = hoptimal.create_study("minimize")   # GP + Expected Improvement by default

def objective(trial):
    x = trial.suggest_float("x", -5.0, 5.0)
    y = trial.suggest_float("y", -5.0, 5.0)
    return (x - 2.0) ** 2 + (y + 1.0) ** 2

study.optimize(objective, n_trials=50)
print(study.best_value, study.best_params)

The Trial API mirrors Optuna's, so migration is mostly mechanical. For a runnable tour (toy problem → Branin convergence plot → real sklearn model → head-to-head vs Optuna) see examples/demo.ipynb.

scikit-learn example

from sklearn.svm import SVC
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from hoptimal.integrations.sklearn import HoptimalSearchCV

pipe = Pipeline([("scaler", StandardScaler()), ("svc", SVC())])
search = HoptimalSearchCV(
    pipe,
    {"svc__C":     ("float", 1e-3, 1e3, {"log": True}),
     "svc__gamma": ("float", 1e-4, 1e0, {"log": True}),
     "svc__kernel":("categorical", ["rbf", "sigmoid"])},
    n_trials=40, cv=5, scoring="accuracy",
)
search.fit(X, y)
print(search.best_score_, search.best_params_)

Visualization & analysis

Install the plotting extras (pip install hoptimal[viz]) to inspect a study with a matplotlib API that mirrors Optuna's:

visualization gallery

from hoptimal import visualization as viz, get_param_importances

viz.plot_optimization_history(study)   # best-so-far convergence
viz.plot_param_importances(study)      # random-forest importances
viz.plot_slice(study)                  # objective vs each parameter
viz.plot_contour(study, params=["x", "y"])
viz.plot_pareto_front(mo_study)        # multi-objective

get_param_importances(study)           # -> {"x": 0.62, "lr": 0.24, ...}

Export every trial to a pandas DataFrame for custom analysis or logging:

df = study.trials_dataframe()
# columns: number, value, datetime_start/complete, duration, state,
#          params_<name>..., user_attrs_<key>...

See the changelog for the full list of changes.

Build from source

With Docker (recommended — builds + tests + validates integrations on clean Linux):

docker build --target core -t hoptimal .          # C++ core + tests + bindings
docker build --target integrations -t hoptimal .  # + sklearn/xgboost/lightgbm/catboost
docker build --target dl -t hoptimal .            # + pytorch/jax/tensorflow (heavy)

Locally (needs a C++20 compiler, CMake, Eigen3; GoogleTest/pybind11 are fetched automatically if absent):

# C++ library + tests
cmake -B build -DHOPTIMAL_BUILD_TESTS=ON
cmake --build build --parallel
ctest --test-dir build --output-on-failure

# Python package
pip install .

How it works

Each trial, hoptimal fits a Gaussian Process to the observations so far, then picks the next point by optimizing an acquisition function over the GP's posterior. The implementation is hand-written C++:

  • GP regression with RBF / Matérn-5/2 kernels using ARD (a separate length-scale per dimension, so anisotropic objectives are modelled correctly); inference via a Cholesky factorization of K + σ²I (with jitter for stability) rather than an explicit inverse.
  • Kernel hyperparameters fitted by maximizing the log marginal likelihood (MAP, with weak log-normal priors that regularize the per-dimension length-scales) via L-BFGS with random restarts.
  • Acquisition — LogEI by default (a numerically-stable log Expected Improvement that doesn't underflow far from data), also UCB / PI — optimized over the normalized [0,1]ᵈ space via a low-discrepancy (Halton) candidate set refined with L-BFGS. The first few trials use a space-filling Halton design before the GP takes over.
  • Categorical parameters are one-hot encoded so unordered categories aren't given a false ordering.

License

MIT — see LICENSE.

Project links

Data verified by PyPI on Jul 8, 2026
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Avatar for danieldema from gravatar.com danieldema

Credits

Author: Daniel Dema

GitHub Statistics

Data verified by PyPI on Jul 8, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

MIT
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Requires

Python >=3.9

Provides Extra

sklearn torch tensorflow jax xgboost lightgbm catboost viz benchmark all

Tags

hyperparameter optimization bayesian-optimization gaussian-process machine-learning automl

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