Bayesian sequential design of computer experiments for quantile set inversion
- URL: http://arxiv.org/abs/2211.01008v5
- Date: Thu, 18 Jul 2024 08:21:58 GMT
- Title: Bayesian sequential design of computer experiments for quantile set inversion
- Authors: Romain Ait Abdelmalek-Lomenech, Julien Bect, Vincent Chabridon, Emmanuel Vazquez,
- Abstract summary: We consider an unknown multivariate function representing a system-such as a complex numerical simulator.
Our objective is to estimate the set of deterministic inputs leading to outputs whose probability is less than a given threshold.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem we propose a Bayesian strategy, based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.
Related papers
- Random Aggregate Beamforming for Over-the-Air Federated Learning in Large-Scale Networks [66.18765335695414]
We consider a joint device selection and aggregate beamforming design with the objectives of minimizing the aggregate error and maximizing the number of selected devices.
To tackle the problems in a cost-effective manner, we propose a random aggregate beamforming-based scheme.
We additionally use analysis to study the obtained aggregate error and the number of the selected devices when the number of devices becomes large.
arXiv Detail & Related papers (2024-02-20T23:59:45Z) - Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences.
Our method is especially suitable for problems with well-specified likelihoods.
We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
arXiv Detail & Related papers (2023-11-08T00:10:21Z) - Efficient Model-Free Exploration in Low-Rank MDPs [76.87340323826945]
Low-Rank Markov Decision Processes offer a simple, yet expressive framework for RL with function approximation.
Existing algorithms are either (1) computationally intractable, or (2) reliant upon restrictive statistical assumptions.
We propose the first provably sample-efficient algorithm for exploration in Low-Rank MDPs.
arXiv Detail & Related papers (2023-07-08T15:41:48Z) - Margin theory for the scenario-based approach to robust optimization in
high dimension [0.0]
This paper deals with the scenario approach to robust optimization.
This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in a problem.
arXiv Detail & Related papers (2023-03-07T13:33:46Z) - Fully Stochastic Trust-Region Sequential Quadratic Programming for
Equality-Constrained Optimization Problems [62.83783246648714]
We propose a sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with objectives and deterministic equality constraints.
The algorithm adaptively selects the trust-region radius and, compared to the existing line-search StoSQP schemes, allows us to utilize indefinite Hessian matrices.
arXiv Detail & Related papers (2022-11-29T05:52:17Z) - Probabilistic learning constrained by realizations using a weak
formulation of Fourier transform of probability measures [0.0]
This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle.
A functional approach is developed on the basis of a weak formulation of the Fourier transform of probability measures.
The presented application in high dimension demonstrates the efficiency and the robustness of the proposed algorithm.
arXiv Detail & Related papers (2022-05-06T08:54:57Z) - Runtime Analysis of Single- and Multi-Objective Evolutionary Algorithms
for Chance Constrained Optimization Problems with Normally Distributed Random
Variables [13.264683014487376]
We study the scenario of components that are independent and Normally distributed.
We show that imposing an additional uniform constraint already leads to local optima.
We prove that this approach can also be used to compute a set of optimal solutions for the chance constrained minimum spanning tree problem.
arXiv Detail & Related papers (2021-09-13T09:24:23Z) - Rare event estimation using stochastic spectral embedding [0.0]
Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems.
We propose a set of modifications that tailor the algorithm to efficiently solve rare event estimation problems.
arXiv Detail & Related papers (2021-06-09T16:10:33Z) - Adaptive Sampling for Best Policy Identification in Markov Decision
Processes [79.4957965474334]
We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model.
The advantages of state-of-the-art algorithms are discussed and illustrated.
arXiv Detail & Related papers (2020-09-28T15:22:24Z) - Stochastic Saddle-Point Optimization for Wasserstein Barycenters [69.68068088508505]
We consider the populationimation barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data.
We employ the structure of the problem and obtain a convex-concave saddle-point reformulation of this problem.
In the setting when the distribution of random probability measures is discrete, we propose an optimization algorithm and estimate its complexity.
arXiv Detail & Related papers (2020-06-11T19:40:38Z) - Variational Bayesian Methods for Stochastically Constrained System
Design Problems [7.347989843033034]
We study system design problems stated as parameterized programs with a chance-constraint set.
We propose a variational Bayes-based method to approximately compute the posterior predictive integral.
arXiv Detail & Related papers (2020-01-06T05:21:39Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.