12,871 research outputs found
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
We present a tutorial on Bayesian optimization, a method of finding the
maximum of expensive cost functions. Bayesian optimization employs the Bayesian
technique of setting a prior over the objective function and combining it with
evidence to get a posterior function. This permits a utility-based selection of
the next observation to make on the objective function, which must take into
account both exploration (sampling from areas of high uncertainty) and
exploitation (sampling areas likely to offer improvement over the current best
observation). We also present two detailed extensions of Bayesian optimization,
with experiments---active user modelling with preferences, and hierarchical
reinforcement learning---and a discussion of the pros and cons of Bayesian
optimization based on our experiences
Bayesian optimization for materials design
We introduce Bayesian optimization, a technique developed for optimizing
time-consuming engineering simulations and for fitting machine learning models
on large datasets. Bayesian optimization guides the choice of experiments
during materials design and discovery to find good material designs in as few
experiments as possible. We focus on the case when materials designs are
parameterized by a low-dimensional vector. Bayesian optimization is built on a
statistical technique called Gaussian process regression, which allows
predicting the performance of a new design based on previously tested designs.
After providing a detailed introduction to Gaussian process regression, we
introduce two Bayesian optimization methods: expected improvement, for design
problems with noise-free evaluations; and the knowledge-gradient method, which
generalizes expected improvement and may be used in design problems with noisy
evaluations. Both methods are derived using a value-of-information analysis,
and enjoy one-step Bayes-optimality
Bayesian optimization for computationally extensive probability distributions
An efficient method for finding a better maximizer of computationally
extensive probability distributions is proposed on the basis of a Bayesian
optimization technique. A key idea of the proposed method is to use extreme
values of acquisition functions by Gaussian processes for the next training
phase, which should be located near a local maximum or a global maximum of the
probability distribution. Our Bayesian optimization technique is applied to the
posterior distribution in the effective physical model estimation, which is a
computationally extensive probability distribution. Even when the number of
sampling points on the posterior distributions is fixed to be small, the
Bayesian optimization provides a better maximizer of the posterior
distributions in comparison to those by the random search method, the steepest
descent method, or the Monte Carlo method. Furthermore, the Bayesian
optimization improves the results efficiently by combining the steepest descent
method and thus it is a powerful tool to search for a better maximizer of
computationally extensive probability distributions.Comment: 13 pages, 5 figure
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