# A bandit-learning approach to multifidelity approximation

arXiv: https://arxiv.org/abs/2103.15342 · HTML: https://mlsanity.com/paper/2103.15342/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 67 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 4 of 4)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A Survey on Practical Applications of Multi-Armed and Contextual Bandits](https://mlsanity.com/paper/1904.10040/) (2019)
- [The Multi-fidelity Multi-armed Bandit](https://mlsanity.com/paper/1610.09726/) (2016)

## Built on by (most cited first, 2 of 2)

- [Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification](https://mlsanity.com/paper/2211.10835/) (2022)
- [When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation](https://mlsanity.com/paper/2609.36704/) (2026)

## Abstract (arXiv)

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 textita 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.