131 research outputs found
The Kalai-Smorodinski solution for many-objective Bayesian optimization
An ongoing aim of research in multiobjective Bayesian optimization is to
extend its applicability to a large number of objectives. While coping with a
limited budget of evaluations, recovering the set of optimal compromise
solutions generally requires numerous observations and is less interpretable
since this set tends to grow larger with the number of objectives. We thus
propose to focus on a specific solution originating from game theory, the
Kalai-Smorodinsky solution, which possesses attractive properties. In
particular, it ensures equal marginal gains over all objectives. We further
make it insensitive to a monotonic transformation of the objectives by
considering the objectives in the copula space. A novel tailored algorithm is
proposed to search for the solution, in the form of a Bayesian optimization
algorithm: sequential sampling decisions are made based on acquisition
functions that derive from an instrumental Gaussian process prior. Our approach
is tested on four problems with respectively four, six, eight, and nine
objectives. The method is available in the Rpackage GPGame available on CRAN at
https://cran.r-project.org/package=GPGame
Bayesian Quantile and Expectile Optimisation
Bayesian optimisation is widely used to optimise stochastic black box
functions. While most strategies are focused on optimising conditional
expectations, a large variety of applications require risk-averse decisions and
alternative criteria accounting for the distribution tails need to be
considered. In this paper, we propose new variational models for Bayesian
quantile and expectile regression that are well-suited for heteroscedastic
settings. Our models consist of two latent Gaussian processes accounting
respectively for the conditional quantile (or expectile) and variance that are
chained through asymmetric likelihood functions. Furthermore, we propose two
Bayesian optimisation strategies, either derived from a GP-UCB or Thompson
sampling, that are tailored to such models and that can accommodate large
batches of points. As illustrated in the experimental section, the proposed
approach clearly outperforms the state of the art
Regret Bounds for Noise-Free Bayesian Optimization
Bayesian optimisation is a powerful method for non-convex black-box
optimization in low data regimes. However, the question of establishing tight
upper bounds for common algorithms in the noiseless setting remains a largely
open question. In this paper, we establish new and tightest bounds for two
algorithms, namely GP-UCB and Thompson sampling, under the assumption that the
objective function is smooth in terms of having a bounded norm in a Mat\'ern
RKHS. Importantly, unlike several related works, we do not consider perfect
knowledge of the kernel of the Gaussian process emulator used within the
Bayesian optimization loop. This allows us to provide results for practical
algorithms that sequentially estimate the Gaussian process kernel parameters
from the available data
Using numerical plant models and phenotypic correlation space to design achievable ideotypes
Numerical plant models can predict the outcome of plant traits modifications
resulting from genetic variations, on plant performance, by simulating
physiological processes and their interaction with the environment.
Optimization methods complement those models to design ideotypes, i.e. ideal
values of a set of plant traits resulting in optimal adaptation for given
combinations of environment and management, mainly through the maximization of
a performance criteria (e.g. yield, light interception). As use of simulation
models gains momentum in plant breeding, numerical experiments must be
carefully engineered to provide accurate and attainable results, rooting them
in biological reality. Here, we propose a multi-objective optimization
formulation that includes a metric of performance, returned by the numerical
model, and a metric of feasibility, accounting for correlations between traits
based on field observations. We applied this approach to two contrasting
models: a process-based crop model of sunflower and a functional-structural
plant model of apple trees. In both cases, the method successfully
characterized key plant traits and identified a continuum of optimal solutions,
ranging from the most feasible to the most efficient. The present study thus
provides successful proof of concept for this enhanced modeling approach, which
identified paths for desirable trait modification, including direction and
intensity.Comment: 25 pages, 5 figures, 2017, Plant, Cell and Environmen
TREGO: a Trust-Region Framework for Efficient Global Optimization
Efficient Global Optimization (EGO) is the canonical form of Bayesian
optimization that has been successfully applied to solve global optimization of
expensive-to-evaluate black-box problems. However, EGO struggles to scale with
dimension, and offers limited theoretical guarantees. In this work, a
trust-region framework for EGO (TREGO) is proposed and analyzed. TREGO
alternates between regular EGO steps and local steps within a trust region. By
following a classical scheme for the trust region (based on a sufficient
decrease condition), the proposed algorithm enjoys global convergence
properties, while departing from EGO only for a subset of optimization steps.
Using extensive numerical experiments based on the well-known COCO {bound
constrained problems}, we first analyze the sensitivity of TREGO to its own
parameters, then show that the resulting algorithm is consistently
outperforming EGO and getting competitive with other state-of-the-art black-box
optimization methods
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