A BANDIT-LEARNING APPROACH TO MULTIFIDELITY APPROXIMATION

Yiming Xu, Vahid Keshavarzzadeh, Robert M. Kirby, Akil Narayan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Multifidelity approximation is an important technique in scientific computation and simulation. In this paper, we introduce a bandit-learning approach for leveraging data of varying fidelities to achieve precise estimates of the parameters of interest. Under a linear model assumption, we formulate a multifidelity approximation as a modified stochastic bandit and analyze the loss for a class of policies that uniformly explore each model before exploiting. Utilizing the estimated conditional mean-squared error, we propose a consistent algorithm, adaptive explore-then-commit (AETC), and establish a corresponding trajectorywise optimality result. These results are then extended to the case of vector-valued responses, where we demonstrate that the algorithm is efficient without the need to worry about estimating high-dimensional parameters. The main advantage of our approach is that we require neither hierarchical model structure nor a priori knowledge of statistical information (e.g., correlations) about or between models. Instead, the AETC algorithm requires only knowledge of which model is a trusted high-fidelity model, along with (relative) computational cost estimates of querying each model. Numerical experiments are provided at the end to support our theoretical findings.

Original languageEnglish
Pages (from-to)A150-A175
JournalSIAM Journal on Scientific Computing
Volume44
Issue number1
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics

Keywords

  • bandit learning
  • consistency
  • linear regression
  • Monte Carlo
  • multifidelity

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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