提出自适应多保真优化算法，无需先验参数即可高效寻优。
Adaptive multi-fidelity optimization with fast learning rates
- 基于代价-偏差函数设计自适应策略，动态权衡计算成本与近似误差。
- 在有限预算下实现更优的简单遗憾率，优于已有方法。
- 无需了解函数光滑性或保真度信息，适合实际应用中的不确定场景。
在多保真优化中，可获得目标函数不同成本的有偏近似。本文研究在有限预算下优化局部光滑函数的问题，需在近似代价与偏差间权衡。我们首先基于代价-偏差函数，推导出不同保真度假设下的简单遗憾下界。随后提出Kometo算法，在无需函数光滑性及保真度先验的前提下，以额外对数因子代价达到最优率，并改进了已有理论保证。最后通过实验验证，该算法在不依赖问题相关参数的情况下，性能优于现有方法。
原文摘要 · Abstract (English)
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.
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