Bayesian Optimization by Density-Ratio Estimation

## BORE: Bayesian Optimization as Density-Ratio Estimation

A minimalistic implementation of BORE: Bayesian Optimization as Density-Ratio Estimation [1] in Python 3 and TensorFlow 2.

### Getting Started

Install with pip:

$pip install "bore[tf]" With support for GPU accelaration: $ pip install "bore[tf-gpu]"

With support for HpBandSter plugin:

\$ pip install "bore[tf,hpbandster]"

### Usage/Examples

This example implements an instantiation of BORE based on a multi-layer perceptron (i.e. a fully-connected feed-forward neural network) classifier.

First we build and compile the classifier model using MaximizableSequential:

from bore.models import MaximizableSequential
from tensorflow.keras.layers import Dense

# build model
classifier = MaximizableSequential()

# compile model
classifier.compile(optimizer="adam", loss="binary_crossentropy")

This syntax should be familiar to anyone who has used a high-level neural network library such as Keras. In fact, MaximizableSequential is simply a subclass of the Sequential class from Keras. More specifically, in addition to inheriting the usual functionalities, it provides the argmax method which finds the input at which the network output is maximized.

Using this method, the standard optimization loop can be implemented as follows:

import numpy as np

features = []
targets = []

# initial design
features.extend(features_init)
targets.extend(targets_init)

for i in range(num_iterations):

# construct classification problem
X = np.vstack(features)
y = np.hstack(targets)

tau = np.quantile(y, q=0.25)
z = np.less(y, tau)

# update classifier
classifier.fit(X, z, epochs=200, batch_size=64)

# suggest new candidate
x_next = classifier.argmax(method="L-BFGS-B", num_start_points=3, bounds=bounds)

# evaluate blackbox function
y_next = blackbox.evaluate(x_next)

# update dataset
features.append(x_next)
targets.append(y_next)

For complete end-to-end scripts and to reproduce our results, take a look at the associated experiments repository.

### Features

• BORE-MLP: BORE based on a multi-layer perceptron (MLP) classifier

• Provides higher-order functions that leverage automatic differentiation to transform Keras models into functions that can easily be optimized by methods in SciPy, not least multi-started quasi-Newton hill-climbing methods such as L-BFGS.

• Integration with the Optuna framework by implementing a Sampler plugin.

### Authors

 Louis Tiao Aaron Klein https://tiao.io/ https://aaronkl.github.io/

### Reference

#### Cite:

@inproceedings{tiao2021-bore,
title={{B}ayesian {O}ptimization by {D}ensity-{R}atio {E}stimation},
author={Tiao, Louis and Klein, Aaron and Archambeau, C\'{e}dric and Bonilla, Edwin V and Seeger, Matthias and Ramos, Fabio},
booktitle={Proceedings of the 38th International Conference on Machine Learning (ICML2021)},
year={2021},
month={July}
}

Copyright (c) 2021, Louis C. Tiao

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

## History

0.1.0 (2019-12-27)

• First release on PyPI.

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