Python库 | bayes-optim-0.2.0.tar.gz

[](https://github.com/wangronin/Bayesian-Optimization/actions) # Bayesian Optimization Library A `Python` implementation of the Bayesian Optimization (BO) algorithm working on decision spaces composed of either real, integer, catergorical variables, or a mixture thereof. Underpinned by surrogate models, BO iteratively proposes candidate solutions using the so-called **acquisition function** which balances exploration with exploitation, and updates the surrogate model with newly observed objective values. This algorithm is designed to optimize **expensive black-box** problems efficiently.  ## Installation You could either install the stable version on `pypi`: ```shell pip install bayes-optim ``` Or, take the lastest version from github: ```shell git clone https://github.com/wangronin/Bayesian-Optimization.git cd Bayesian-Optimization && python setup.py install --user ``` ## Example For real-valued search variables, the simplest usage is via the `fmin` function: ```python from bayes_optim import fmin def f(x): return sum(x ** 2) minimum = fmin(f, [-5] * 2, [5] * 2, max_FEs=30, seed=42) ``` And you could also have much finer control over most ingredients of BO, e.g., the surrogate model and acquisition functions. Please see the example below: ```python from bayes_optim import BO, RealSpace from bayes_optim.Surrogate import GaussianProcess dim = 5 space = RealSpace([-5, 5]) * dim # create the search space # hyperparameters of the GPR model thetaL = 1e-10 * (ub - lb) * np.ones(dim) thetaU = 10 * (ub - lb) * np.ones(dim) model = GaussianProcess( # create the GPR model thetaL=thetaL, thetaU=thetaU ) opt = BO( search_space=space, obj_fun=fitness, model=model, DoE_size=5, # number of initial sample points max_FEs=50, # maximal function evaluation verbose=True ) opt.run() ``` For more detailed usage and exmaples, please check out our [wiki page](https://github.com/wangronin/Bayesian-Optimization/wiki). ## Features This implementation differs from alternative packages/libraries in the following features: * **Parallelization**, also known as _batch-sequential optimization_, for which several different approaches are implemented here. * **Moment-Generating Function of the improvment** (MGFI) [WvSEB17a] is a recently proposed acquistion function, which implictly controls the exploration-exploitation trade-off. * **Mixed-Integer Evolution Strategy** for optimizing the acqusition function, which is enabled when the search space is a mixture of real, integer, and categorical variables. ## Project Structure * `bayes-optim/SearchSpace.py`: implementation of the search/decision space. * `bayes-optim/base.py`: the base class of Bayesian Optimization. * `bayes-optim/AcquisitionFunction.py`: the implemetation of acquisition functions (see below for the list of implemented ones). * `bayes-optim/Surrogate`: we implemented the Gaussian Process Regression (GPR) and Random Forest (RF). * `bayes-optim/BayesOpt.py` contains several BO variants: * `BO`: noiseless + sequential * `ParallelBO`: noiseless + parallel (a.k.a. batch-sequential) * `AnnealingBO`: noiseless + parallel + annealling [WEB18] * `SelfAdaptiveBO`: noiseless + parallel + self-adaptive [WEB19] * `NoisyBO`: noisy + parallel * `bayes-optim/Extension.py` is meant to include the lastest developments that are not extensively tested: * `PCABO`: noiseless + parallel + PCA-assisted dimensionality reduction [RaponiWBBD20] **[Under Construction]** * `MultiAcquisitionBO`: noiseless + parallelization with multiple different acquisition functions **[Under Construction]** <!-- * `optimizer/`: the optimization algorithm to maximize the infill-criteria, two algorithms are implemented: 1. **CMA-ES**: Covariance Martix Adaptation Evolution Strategy for _continuous_ optimization problems. 2. **MIES**: Mixed-Integer Evolution Strategy for mixed-integer/categorical optimization problems. --> ## Acquisition Functions The following infill-criteria are implemented in the library: * _Expected Improvement_ (EI) * Probability of Improvement (PI) / Probability of Improvement * _Upper Confidence Bound_ (UCB) * _Moment-Generating Function of Improvement_ (MGFI) * _Generalized Expected Improvement_ (GEI) **[Under Construction]** For sequential working mode, Expected Improvement is used by default. For parallelization mode, MGFI is enabled by default. ## Surrogate Model The meta (surrogate)-model used in Bayesian optimization. The basic requirement for such a model is to provide the uncertainty quantification (either empirical or theorerical) for the prediction. To easily handle the categorical data, __random forest__ model is used by default. The implementation here is based the one in _scikit-learn_, with modifications on uncertainty quantification. ## A brief Introduction to Bayesian Optimization Bayesian Optimization [Moc74, JSW98] (BO) is a sequential optimization strategy originally proposed to solve the single-objective black-box optimiza-tion problem that is costly to evaluate. Here, we shall restrict our discussion to the single-objective case. BO typically starts with sampling an initial design of experiment (DoE) of size, X={x₁,x₂,...,x_n}, which is usually generated by simple random sampling, Latin Hypercube Sampling [SWN03], or the more sophisticated low-discrepancy sequence [Nie88] (e.g., Sobol sequences). Taking the initial DoE X and its corresponding objective value, Y={f(x₁), f(x₂),..., f(x_n)} ⊆ ℝ, we proceed to construct a statistical model M describing the probability distribution of the objective function conditioned onthe initial evidence, namely Pr(f|X,Y). In most application scenarios of BO, there is a lack of a priori knowledge about f and therefore nonparametric models (e.g., Gaussian process regression or random forest) are commonly chosen for M, which gives rise to a predictor f'(x) for all x ∈ X and an uncertainty quantification s'(x) that estimates, for instance, the mean squared error of the predic-tion E(f'(x)−f(x))². Based on f' and s', promising points can be identified via the so-called acquisition function which balances exploitation with exploration of the optimization process. <!-- Bayesian optimization is __sequential design strategy__ that does not require the derivatives of the objective function and is designed to solve expensive global optimization problems. Compared to alternative optimization algorithms (or other design of experiment methods), the very distinctive feature of this method is the usage of a __posterior distribution__ over the (partially) unknown objective function, which is obtained via __Bayesian inference__. This optimization framework is proposed by Jonas Mockus and Antanas Zilinskas, et al. Formally, the goal is to approach the global optimum, using a sequence of variables: $$\mathbf{x}_1,\mathbf{x}_2, \ldots, \mathbf{x}_n \in S \subseteq \mathbb{R}^d,$$ which resembles the search sequence in stochastic hill-climbing, simulated annealing and (1+1)-strategies. The only difference is that such a sequence is __not__ necessarily random and it is actually deterministic (in principle) for Bayesian optimization. In order to approach the global optimum, this algorithm iteratively seeks for an optimal choice as the next candidate variable adn the choice can be considered as a decision function: \[\mathbf{x}_{n+1} = d_n\left(\{\mathbf{x}_i\}_{i=1}^n, \{y_i\}_{i=1}^n \right), \quad y_i = f(\mathbf{x}_i) + \varepsilon,\] meaning that it takes the history of the optimization in order to make a decision. The quality of a decision can be measured by the following loss function that is the optimality error or optimality gap: $$\epsilon