A bandit-learning approach to multifidelity approximation

• URL: http://arxiv.org/abs/2103.15342v1
• Date: Mon, 29 Mar 2021 05:29:35 GMT
• Title: A bandit-learning approach to multifidelity approximation
• Authors: Yiming Xu, Vahid Keshavarzzadeh, Robert M. Kirby, Akil Narayan
• Abstract summary: Multifidelity approximation is an important technique in scientific computation and simulation. We introduce a bandit-learning approach for leveraging data of varying fidelities to achieve precise estimates.
• Score: 7.960229223744695
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 trajectory-wise 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 \textit{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.

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