Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different than those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP) based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 4x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

翻译：随机数值线性代数（RandNLA）算法在处理高维计算问题中表现出色，不仅具有高水平的经验性能，还具备强大的概率保证。然而，用户需要设置与传统数值线性代数（NLA）不同的多种算法特定调参参数，这增加了其实际应用的复杂性。本文证明，基于代理模型的自动调参方法可有效解决RandNLA算法中参数选择的基本问题。具体而言，我们针对基于草图-预处理（SAP）的随机最小二乘方法（现代RandNLA中最成功的案例之一）开展了详细的代理模型调参研究。实验结果表明，与随机搜索相比，我们的代理模型调参方法能以更少的调参成本（参数配置试验次数减少约4倍）实现接近最优的性能。此外，尽管实验聚焦于最小二乘问题，但我们的结果展示了一种适用于任何RandNLA算法的通用自动调参流程。