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.

翻译：多纤维近似是科学计算和模拟的一个重要技术。 在本文中, 我们引入了一种土匪学习方法, 来利用不同忠诚的数据, 以精确估计利益参数。 在一条线性模型假设下, 我们将多纤维近近似制成一个修改过的随机土匪, 并分析在开发之前统一探索每个模型的某类政策的损失。 利用估计的有条件平均差错, 我们建议一种一致的算法, 适应性探索- 后传播( AETC), 并建立一个相应的轨迹最佳性最佳效果。 这些结果随后推广到矢量值反应中, 我们证明算法是有效的, 不需要担心估计高维度参数。 我们方法的主要优点是, 我们不需要等级模型结构, 也不需要对各种模型的统计信息( 例如, 相关关系 ) 进行认知。 相反, AETC 算法只要求知道哪个模型是可信的高纤维模型, 以及( 相对) 计算成本估算每个模型的计算结果。 Numericalal 是在最后提供的。