42,329 research outputs found
Bayesian Optimization with Conformal Prediction Sets
Bayesian optimization is a coherent, ubiquitous approach to decision-making
under uncertainty, with applications including multi-arm bandits, active
learning, and black-box optimization. Bayesian optimization selects decisions
(i.e. objective function queries) with maximal expected utility with respect to
the posterior distribution of a Bayesian model, which quantifies reducible,
epistemic uncertainty about query outcomes. In practice, subjectively
implausible outcomes can occur regularly for two reasons: 1) model
misspecification and 2) covariate shift. Conformal prediction is an uncertainty
quantification method with coverage guarantees even for misspecified models and
a simple mechanism to correct for covariate shift. We propose conformal
Bayesian optimization, which directs queries towards regions of search space
where the model predictions have guaranteed validity, and investigate its
behavior on a suite of black-box optimization tasks and tabular ranking tasks.
In many cases we find that query coverage can be significantly improved without
harming sample-efficiency.Comment: For code, see
https://www.github.com/samuelstanton/conformal-bayesopt.gi
GPflowOpt: A Bayesian Optimization Library using TensorFlow
A novel Python framework for Bayesian optimization known as GPflowOpt is
introduced. The package is based on the popular GPflow library for Gaussian
processes, leveraging the benefits of TensorFlow including automatic
differentiation, parallelization and GPU computations for Bayesian
optimization. Design goals focus on a framework that is easy to extend with
custom acquisition functions and models. The framework is thoroughly tested and
well documented, and provides scalability. The current released version of
GPflowOpt includes some standard single-objective acquisition functions, the
state-of-the-art max-value entropy search, as well as a Bayesian
multi-objective approach. Finally, it permits easy use of custom modeling
strategies implemented in GPflow
Learning Multiple Defaults for Machine Learning Algorithms
The performance of modern machine learning methods highly depends on their
hyperparameter configurations. One simple way of selecting a configuration is
to use default settings, often proposed along with the publication and
implementation of a new algorithm. Those default values are usually chosen in
an ad-hoc manner to work good enough on a wide variety of datasets. To address
this problem, different automatic hyperparameter configuration algorithms have
been proposed, which select an optimal configuration per dataset. This
principled approach usually improves performance, but adds additional
algorithmic complexity and computational costs to the training procedure. As an
alternative to this, we propose learning a set of complementary default values
from a large database of prior empirical results. Selecting an appropriate
configuration on a new dataset then requires only a simple, efficient and
embarrassingly parallel search over this set. We demonstrate the effectiveness
and efficiency of the approach we propose in comparison to random search and
Bayesian Optimization
Shrinkage Estimators in Online Experiments
We develop and analyze empirical Bayes Stein-type estimators for use in the
estimation of causal effects in large-scale online experiments. While online
experiments are generally thought to be distinguished by their large sample
size, we focus on the multiplicity of treatment groups. The typical analysis
practice is to use simple differences-in-means (perhaps with covariate
adjustment) as if all treatment arms were independent. In this work we develop
consistent, small bias, shrinkage estimators for this setting. In addition to
achieving lower mean squared error these estimators retain important
frequentist properties such as coverage under most reasonable scenarios. Modern
sequential methods of experimentation and optimization such as multi-armed
bandit optimization (where treatment allocations adapt over time to prior
responses) benefit from the use of our shrinkage estimators. Exploration under
empirical Bayes focuses more efficiently on near-optimal arms, improving the
resulting decisions made under uncertainty. We demonstrate these properties by
examining seventeen large-scale experiments conducted on Facebook from April to
June 2017
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