Bayesian Quadrature Optimization is a software package to perform Bayesian optimization. In particular, it includes the algorithm Bayesian Quadrature Optimization from the paper 'Bayesian Optimization with Expensive Integrands' by Saul Toscano-Palmerin and Peter Frazier.
In the project root, run:
make env
make test
The algorithms implemented maximize the objective function.
- Steps to use BQO:
- Import library:
from stratified_bayesian_optimization.services.bgo import bgo
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Define the objective function g(x) where x are the arguments of the function as a list, and the refunction returns [float].
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For BQO define the integrand function f(x) where x are the arguments of the function as a list, and the function returns [float]. If the function is noisy, include the parameter n_samples, f(x, n_samples), and the function returns [(float) value of function, (float) variance].
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Define the bounds of the domain of x as a list: [[(float) lower_bound, (float) upper_bound]].
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For BQO define the bounds_domain_w as a list: [[(float) lower_bound, (float) upper_bound] or [(float) range]]. In the second case, the list represents the points of the domain of that entry (e.g. when W is finite).
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Define type_bounds as a list of size equal to the dimension of the domain of the integrand of 0's and 1's. If the entry is 0, it means that the bounds are an interval: [lower_bound, upper_bound]. If the entry is 1, it means that the bounds contains all the possible points of that entry of the domain.
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Define (str) name_method to choose the BO method to optimize the function. For example, name_method = 'bqo' or 'ei'.
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n_iterations is the number of points chosen by the BO method.
- Optional Arguments:
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(Optional) (int) random_seed to run the BO method.
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(Optional) (int) n_training is the number of training points for the BO method.
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(Optional) Define problem_name as a string. If None, problem_name='user_problem'
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(Optional) (int) n_restarts, Number of starting points to optimize the acquisition function. Default is 10.
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(Optional) (int) n_restarts_mean, Number of starting points to optimize the posterior mean. Default is 100.
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(Optional) (int) n_best_restarts_mean, Number of best starting points chosen from the n_restart points. Default is 10.
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(Optional) (int) maxepoch: Maximum number of iterations of the SGD when optimizing the acquisition function. Default is 50.
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(Optional) (int) maxepoch_mean: Maxepoch for the optimization of the posterior mean. Default is 50.
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(Optional) (int) n_burning: Number of burnings samples for slice sampling. Default is 500.
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(Optional) (int) thinning: Thinning parameter for slice sampling to obtain a sample of hyperparameters. Default is 50.
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(Optional) (int) default_n_samples_parameters: Number of samples of Z for the discretization-free estimation of the BQO. Default is 100.
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(Optional) (int) default_n_samples: Number of samples of hyperparameters to estimate BQO. Default is 20.
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(Optional) (str) distribution: probability distribution for the Bayesian quadrature (i.e. the distribution of W). Default: 'uniform_finite' when there are tasks, and 'gamma' when there are no tasks. The other possible distributions are 'exponential' and 'weighted_uniform_finite'. Additional distributions should be coded.
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(Optional) parameters_distribution: {str: float}
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(Optional) (boolean) noise: True if the evaluations of the integrand function are noisy. Default value is False.
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(Optional) (int) n_samples_noise: If noise is true, we take n_samples of the function to estimate its value. Default vale is 0.
- Run BQO:
sol = bgo(
g, bounds_domain_x, integrand_function=f, bounds_domain_w=bounds_domain_w, type_bounds=type_bounds,
name_method=name_method, n_iterations=n_iterations, random_seed=random_seed, n_training=n_training,
problem_name=problem_name, n_restarts=n_restarts, n_restarts_mean=n_restarts_mean,
n_best_restarts_mean=n_best_restarts_mean, maxepoch=maxepoch, maxepoch_mean=maxepoch_mean,
n_burning=n_burning, thinning=thinning, default_n_samples_parameters=default_n_samples_parameters,
default_n_samples=default_n_samples, distribution=distribution, parameters_distribution=parameters_distribution,
noise=noise, n_samples_noise=n_samples_noise)
- The output sol is a dictionary. The entry 'optimal_solution' contains the solution given by the BO algorithm, and 'optimal_value' is the objective function evaluated at the 'optimal_solution'.
- Files generated:
- The training data is written in problems/problem_name/data
- The Guassian process model is written as a json file in data/gp_models/problem_name. The entry 'data' contains all the training data plus the points that have been chosen by the Bayesian optimization algorithm.
- The results of the algorithm are written in problems/problem_name/partial_results
Examples can be found here
Consider a queuing simulation based on New York City’s Citi Bike system in which system users may remove an available bike from a station at one location within the city and ride it to a station with an available dock in some other location. The optimization problem that we consider is the allocation of a constrained number of bikes (6000) to available docks within the city at the start of rush hour, so as to minimize, in simulation, the expected number of potential trips in which the rider could not find an available bike at their preferred origination station, or could not find an available dock at their preferred destination station.
In this problem, we choose the initial inventory levels of the products sold, each with certain cost and price, which are assumed given. Our goal is to optimize profit.