57 research outputs found
A Bayesian Approach to Computer Model Calibration and Model-Assisted Design
Computer models of phenomena that are difficult or impossible to study directly are critical for enabling research and assisting design in many areas. In order to be effective, computer models must be calibrated so that they accurately represent the modeled phenomena. There exists a rich variety of methods for computer model calibration that have been developed in recent decades. Among the desiderata of such methods is a means of quantifying remaining uncertainty after calibration regarding both the values of the calibrated model inputs and the model outputs. Bayesian approaches to calibration have met this need in recent decades. However, limitations remain. Whereas in model calibration one finds point estimates or distributions of calibration inputs in order to induce the model to reflect reality accurately, interest in a computer model often centers primarily on its use for model-assisted design, in which the goal is to find values for design inputs to induce the modeled system to approximate some target outcome. Existing Bayesian approaches are limited to the first of these two tasks. The present work develops an approach adapting Bayesian methods for model calibration for application in model-assisted design. The approach retains the benefits of Bayesian calibration in accounting for and quantifying all sources of uncertainty. It is capable of generating a comprehensive assessment of the Pareto optimal inputs for a multi-objective optimization problem. The present work shows that this approach can apply as a method for model-assisted design using a previously calibrated system, and can also serve as a method for model-assisted design using a model that still requires calibration, accomplishing both ends simultaneously
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
qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling
Classical evolutionary approaches for multiobjective optimization are quite
effective but incur a lot of queries to the objectives; this can be prohibitive
when objectives are expensive oracles. A sample-efficient approach to solving
multiobjective optimization is via Gaussian process (GP) surrogates and
Bayesian optimization (BO). Multiobjective Bayesian optimization (MOBO)
involves the construction of an acquisition function which is optimized to
acquire new observation candidates. This ``inner'' optimization can be hard due
to various reasons: acquisition functions being nonconvex, nondifferentiable
and/or unavailable in analytical form; the success of MOBO heavily relies on
this inner optimization. We do away with this hard acquisition function
optimization step and propose a simple, but effective, Thompson sampling based
approach () where new candidate(s) are chosen from the Pareto
frontier of random GP posterior sample paths obtained by solving a much cheaper
multiobjective optimization problem. To further improve computational
tractability in higher dimensions we propose an automated active set of
candidates selection combined with a Nystr\"{o}m approximation. Our approach
applies to arbitrary GP prior assumptions and demonstrates strong empirical
performance over the state of the art, both in terms of accuracy and
computational efficiency, on synthetic as well as real-world experiments.Comment: 12 pages, 4 figure
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
Fantasizing with Dual GPs in Bayesian Optimization and Active Learning
Gaussian processes (GPs) are the main surrogate functions used for sequential
modelling such as Bayesian Optimization and Active Learning. Their drawbacks
are poor scaling with data and the need to run an optimization loop when using
a non-Gaussian likelihood. In this paper, we focus on `fantasizing' batch
acquisition functions that need the ability to condition on new fantasized data
computationally efficiently. By using a sparse Dual GP parameterization, we
gain linear scaling with batch size as well as one-step updates for
non-Gaussian likelihoods, thus extending sparse models to greedy batch
fantasizing acquisition functions.Comment: In the 2022 NeurIPS Workshop on Gaussian Processes, Spatiotemporal
Modeling, and Decision-making System
- …