In multi-fidelity optimization, biased approximations of varying costs of the target function are available. This paper studies the problem of optimizing a locally smooth function with a limited budget, where the learner has to make a tradeoff between the cost and the bias of these approximations. We first prove lower bounds for the simple regret under different assumptions on the fidelities, based on a cost-to-bias function. We then present the Kometo algorithm which achieves, with additional logarithmic factors, the same rates without any knowledge of the function smoothness and fidelity assumptions, and improves previously proven guarantees. We finally empirically show that our algorithm outperforms previous multi-fidelity optimization methods without the knowledge of problem-dependent parameters.

翻译：在多保真度优化中，目标函数的具有不同成本的有偏近似是可用的。本文研究了在有限预算下优化局部光滑函数的问题，其中学习者需在这些近似的成本与偏差之间进行权衡。我们首先基于成本-偏差函数，证明了在不同保真度假设下简单遗憾的下界。接着，我们提出了Kometo算法，该算法在额外对数因子条件下，无需任何关于函数光滑性和保真度假设的知识即可达到相同的速率，并改进了先前已证明的保证。最后，我们通过实验表明，我们的算法在无需问题相关参数知识的情况下，优于以往的多保真度优化方法。