7 research outputs found
Bayesian optimization using sequential Monte Carlo
We consider the problem of optimizing a real-valued continuous function
using a Bayesian approach, where the evaluations of are chosen sequentially
by combining prior information about , which is described by a random
process model, and past evaluation results. The main difficulty with this
approach is to be able to compute the posterior distributions of quantities of
interest which are used to choose evaluation points. In this article, we decide
to use a Sequential Monte Carlo (SMC) approach
Calibration and improved prediction of computer models by universal Kriging
This paper addresses the use of experimental data for calibrating a computer
model and improving its predictions of the underlying physical system. A global
statistical approach is proposed in which the bias between the computer model
and the physical system is modeled as a realization of a Gaussian process. The
application of classical statistical inference to this statistical model yields
a rigorous method for calibrating the computer model and for adding to its
predictions a statistical correction based on experimental data. This
statistical correction can substantially improve the calibrated computer model
for predicting the physical system on new experimental conditions. Furthermore,
a quantification of the uncertainty of this prediction is provided. Physical
expertise on the calibration parameters can also be taken into account in a
Bayesian framework. Finally, the method is applied to the thermal-hydraulic
code FLICA 4, in a single phase friction model framework. It allows to improve
the predictions of the thermal-hydraulic code FLICA 4 significantly
A Bayesian approach to constrained single- and multi-objective optimization
This article addresses the problem of derivative-free (single- or
multi-objective) optimization subject to multiple inequality constraints. Both
the objective and constraint functions are assumed to be smooth, non-linear and
expensive to evaluate. As a consequence, the number of evaluations that can be
used to carry out the optimization is very limited, as in complex industrial
design optimization problems. The method we propose to overcome this difficulty
has its roots in both the Bayesian and the multi-objective optimization
literatures. More specifically, an extended domination rule is used to handle
objectives and constraints in a unified way, and a corresponding expected
hyper-volume improvement sampling criterion is proposed. This new criterion is
naturally adapted to the search of a feasible point when none is available, and
reduces to existing Bayesian sampling criteria---the classical Expected
Improvement (EI) criterion and some of its constrained/multi-objective
extensions---as soon as at least one feasible point is available. The
calculation and optimization of the criterion are performed using Sequential
Monte Carlo techniques. In particular, an algorithm similar to the subset
simulation method, which is well known in the field of structural reliability,
is used to estimate the criterion. The method, which we call BMOO (for Bayesian
Multi-Objective Optimization), is compared to state-of-the-art algorithms for
single- and multi-objective constrained optimization
Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization
This work presents a new procedure for obtaining predictive distributions in
the context of Gaussian process (GP) modeling, with a relaxation of the
interpolation constraints outside some ranges of interest: the mean of the
predictive distributions no longer necessarily interpolates the observed values
when they are outside ranges of interest, but are simply constrained to remain
outside. This method called relaxed Gaussian process (reGP) interpolation
provides better predictive distributions in ranges of interest, especially in
cases where a stationarity assumption for the GP model is not appropriate. It
can be viewed as a goal-oriented method and becomes particularly interesting in
Bayesian optimization, for example, for the minimization of an objective
function, where good predictive distributions for low function values are
important. When the expected improvement criterion and reGP are used for
sequentially choosing evaluation points, the convergence of the resulting
optimization algorithm is theoretically guaranteed (provided that the function
to be optimized lies in the reproducing kernel Hilbert spaces attached to the
known covariance of the underlying Gaussian process). Experiments indicate that
using reGP instead of stationary GP models in Bayesian optimization is
beneficial
Sequential search strategies based on kriging
This manuscript has been written to obtain the French Habilitation Ă Diriger des Recherches. It is not intended to provide new academic results nor should it be considered as a reference textbook. Instead, this manuscript is a brief (and incomplete) summary of my teaching and research activities. You will find in this manuscript a compilation of some articles in which I had a significant contribution, together with some introductory paragraphs about sequential search strategies based on kriging