使用高斯过程进行全局优化的Python实现。_Python_下载.zip

<div align="center"> <img src="https://github.com/fmfn/BayesianOptimization/blob/master/examples/func.png"><br><br> </div> # Bayesian Optimization  [](https://codecov.io/github/fmfn/BayesianOptimization?branch=master) [](https://pypi.python.org/pypi/bayesian-optimization) Pure Python implementation of bayesian global optimization with gaussian processes. * PyPI (pip): ```console $ pip install bayesian-optimization ``` * Conda from conda-forge channel: ```console $ conda install -c conda-forge bayesian-optimization ``` This is a constrained global optimization package built upon bayesian inference and gaussian process, that attempts to find the maximum value of an unknown function in as few iterations as possible. This technique is particularly suited for optimization of high cost functions, situations where the balance between exploration and exploitation is important. ## Quick Start See below for a quick tour over the basics of the Bayesian Optimization package. More detailed information, other advanced features, and tips on usage/implementation can be found in the [examples](https://github.com/fmfn/BayesianOptimization/tree/master/examples) folder. I suggest that you: - Follow the [basic tour notebook](https://github.com/fmfn/BayesianOptimization/blob/master/examples/basic-tour.ipynb) to learn how to use the package's most important features. - Take a look at the [advanced tour notebook](https://github.com/fmfn/BayesianOptimization/blob/master/examples/advanced-tour.ipynb) to learn how to make the package more flexible, how to deal with categorical parameters, how to use observers, and more. - Check out this [notebook](https://github.com/fmfn/BayesianOptimization/blob/master/examples/visualization.ipynb) with a step by step visualization of how this method works. - To understand how to use bayesian optimization when additional constraints are present, see the [constrained optimization notebook](https://github.com/fmfn/BayesianOptimization/blob/master/examples/constraints.ipynb). - Explore this [notebook](https://github.com/fmfn/BayesianOptimization/blob/master/examples/exploitation_vs_exploration.ipynb) exemplifying the balance between exploration and exploitation and how to control it. - Go over this [script](https://github.com/fmfn/BayesianOptimization/blob/master/examples/sklearn_example.py) for examples of how to tune parameters of Machine Learning models using cross validation and bayesian optimization. - Explore the [domain reduction notebook](https://github.com/fmfn/BayesianOptimization/blob/master/examples/domain_reduction.ipynb) to learn more about how search can be sped up by dynamically changing parameters' bounds. - Finally, take a look at this [script](https://github.com/fmfn/BayesianOptimization/blob/master/examples/async_optimization.py) for ideas on how to implement bayesian optimization in a distributed fashion using this package. ## How does it work? Bayesian optimization works by constructing a posterior distribution of functions (gaussian process) that best describes the function you want to optimize. As the number of observations grows, the posterior distribution improves, and the algorithm becomes more certain of which regions in parameter space are worth exploring and which are not, as seen in the picture below.  As you iterate over and over, the algorithm balances its needs of exploration and exploitation taking into account what it knows about the target function. At each step a Gaussian Process is fitted to the known samples (points previously explored), and the posterior distribution, combined with a exploration strategy (such as UCB (Upper Confidence Bound), or EI (Expected Improvement)), are used to determine the next point that should be explored (see the gif below).  This process is designed to minimize the number of steps required to find a combination of parameters that are close to the optimal combination. To do so, this method uses a proxy optimization problem (finding the maximum of the acquisition function) that, albeit still a hard problem, is cheaper (in the computational sense) and common tools can be employed. Therefore Bayesian Optimization is most adequate for situations where sampling the function to be optimized is a very expensive endeavor. See the references for a proper discussion of this method. This project is under active development, if you find a bug, or anything that needs correction, please let me know. Basic tour of the Bayesian Optimization package =============================================== ## 1. Specifying the function to be optimized This is a function optimization package, therefore the first and most important ingredient is, of course, the function to be optimized. **DISCLAIMER:** We know exactly how the output of the function below depends on its parameter. Obviously this is just an example, and you shouldn't expect to know it in a real scenario. However, it should be clear that you don't need to. All you need in order to use this package (and more generally, this technique) is a function `f` that takes a known set of parameters and outputs a real number. ```python def black_box_function(x, y): """Function with unknown internals we wish to maximize. This is just serving as an example, for all intents and purposes think of the internals of this function, i.e.: the process which generates its output values, as unknown. """ return -x ** 2 - (y - 1) ** 2 + 1 ``` ## 2. Getting Started All we need to get started is to instantiate a `BayesianOptimization` object specifying a function to be optimized `f`, and its parameters with their corresponding bounds, `pbounds`. This is a constrained optimization technique, so you must specify the minimum and maximum values that can be probed for each parameter in order for it to work ```python from bayes_opt import BayesianOptimization # Bounded region of parameter space pbounds = {'x': (2, 4), 'y': (-3, 3)} optimizer = BayesianOptimization( f=black_box_function, pbounds=pbounds, random_state=1, ) ``` The BayesianOptimization object will work out of the box without much tuning needed. The main method you should be aware of is `maximize`, which does exactly what you think it does. There are many parameters you can pass to maximize, nonetheless, the most important ones are: - `n_iter`: How many steps of bayesian optimization you want to perform. The more steps the more likely to find a good maximum you are. - `init_points`: How many steps of **random** exploration you want to perform. Random exploration can help by diversifying the exploration space. ```python optimizer.maximize( init_points=2, n_iter=3, ) ``` | iter | target | x | y | ------------------------------------------------- | 1 | -7.135 | 2.834 | 1.322 | | 2 | -7.78 | 2.0 | -1.186 | | 3 | -19.0 | 4.0 | 3.0 | | 4 | -16.3 | 2.378 | -2.413 | | 5 | -4.441 | 2.105 | -0.005822 | ================================================= The best combination of parameters and target value found can be accessed via the property `optimizer.max`. ```python print(optimizer.max) >>> {'target': -4.441293113411222, 'params': {'y': -0.005822117636089974, 'x': 2.104665051994087}} ``` While the list of all parameters probed and their corresponding target values is available via the property `optimizer.res`. ```python for i, res in enumerate(optimizer.res): print("Iteration {}: \n\t{}".for