A supermartingale approach to Gaussian process based sequential design of experiments
Gaussian process (GP) models have become a well-established frameworkfor the adaptive design of costly experiments, and notably of computerexperiments. GP-based sequential designs have been found practicallyefficient for various objectives, such as global optimization(estimating the global maximum or maximizer(s) of a function),reliability analysis (estimating a probability of failure) or theestimation of level sets and excursion sets. In this paper, we studythe consistency of an important class of sequential designs, known asstepwise uncertainty reduction (SUR) strategies. Our approach relieson the key observation that the sequence of residual uncertaintymeasures, in SUR strategies, is generally a supermartingale withrespect to the filtration generated by the observations. Thisobservation enables us to establish generic consistency results for abroad class of SUR strategies. The consistency of several popularsequential design strategies is then obtained by means of this generalresult. Notably, we establish the consistency of two SUR strategiesproposed by Bect, Ginsbourger, Li, Picheny and Vazquez (Stat. Comp.,2012)---to the best of our knowledge, these are the first proofs ofconsistency for GP-based sequential design algorithms dedicated to theestimation of excursion sets and their measure. We also establish anew, more general proof of consistency for the expected improvementalgorithm for global optimization which, unlike previous results inthe literature, applies to any GP with continuous sample paths.
Code (0)
등록된 구현이 없습니다.
Tasks
global-optimizationSimilar Papers 제목 키워드 기반
Consistency of some sequential experimental design strategies for excursion set estimation based on vector-valued Gaussian processes
We tackle the extension to the vector-valued case of consistency results for Stepwise Uncertainty Reduction sequential experimental design strategies established in [Bect et al., A supermartingale approach to Gaussian pr…
Experimental DesignGaussian ProcessesThe extended Ville's inequality for nonintegrable nonnegative supermartingales
Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we derive a key maximal inequality foreshado…
E-detectors: a nonparametric framework for sequential change detection
Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new an…
Change DetectionComputational EfficiencySCOPE: Sequential Conformal Probing for Reliable OOD Rejection in LLM Services
Rejecting inputs outside the defined in-distribution (IND) service scope is critical for large language model (LLM) services, where unsupported requests should be filtered before full generation. Existing out-of-distribu…
Fast and Provably Accurate Sequential Designs using Hilbert Space Gaussian Processes
Gaussian processes are widely used for accurate emulation of unknown surfaces in sequential design of expensive simulation experiments. Integrated mean squared error (IMSE) is an effective acquisition function for sequen…
Gaussian Processes