James W. Demmel

Amal Khabou, James W. Demmel, Laura Grigori et al.

We present the LU decomposition with panel rank revealing pivoting (LU_PRRP), an LU factorization algorithm based on strong rank revealing QR panel factorization. LU_PRRP is more stable than Gaussian elimination with partial pivoting (GEPP). Our extensive numerical experiments show that the new factorization scheme is as numerically stable as GEPP in practice, but it is more resistant to pathological cases and easily solves the Wilkinson matrix and the Foster matrix. We also present CALU_PRRP, a communication avoiding version of LU_PRRP that minimizes communication. CALU_PRRP is based on tournament pivoting, with the selection of the pivots at each step of the tournament being performed via strong rank revealing QR factorization. CALU_PRRP is more stable than CALU, the communication avoiding version of GEPP. CALU_PRRP is also more stable in practice and is resistant to pathological cases on which GEPP and CALU fail.

Younghyun Cho, James W. Demmel, Michał Dereziński et al.

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.

Hengrui Luo, Younghyun Cho, James W. Demmel et al.

This paper presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture's integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.

Hengrui Luo, James W. Demmel, Younghyun Cho et al.

Building surrogate models is one common approach when we attempt to learn unknown black-box functions. Bayesian optimization provides a framework which allows us to build surrogate models based on sequential samples drawn from the function and find the optimum. Tuning algorithmic parameters to optimize the performance of large, complicated "black-box" application codes is a specific important application, which aims at finding the optima of black-box functions. Within the Bayesian optimization framework, the Gaussian process model produces smooth or continuous sample paths. However, the black-box function in the tuning problem is often non-smooth. This difficult tuning problem is worsened by the fact that we usually have limited sequential samples from the black-box function. Motivated by these issues encountered in tuning, we propose a novel additive Gaussian process model called clustered Gaussian process (cGP), where the additive components are induced by clustering. In the examples we studied, the performance can be improved by as much as 90% among repetitive experiments. By using this surrogate model, we want to capture the non-smoothness of the black-box function. In addition to an algorithm for constructing this model, we also apply the model to several artificial and real applications to evaluate it.

Wissam M. Sid-Lakhdar, Mohsen Mahmoudi Aznaveh, Xiaoye S. Li et al.

Multitask learning and transfer learning have proven to be useful in the field of machine learning when additional knowledge is available to help a prediction task. We aim at deriving methods following these paradigms for use in autotuning, where the goal is to find the optimal performance parameters of an application treated as a black-box function. We show comparative results with state-of-the-art autotuning techniques. For instance, we observe an average $1.5x$ improvement of the application runtime compared to the OpenTuner and HpBandSter autotuners. We explain how our approaches can be more suitable than some state-of-the-art autotuners for the tuning of any application in general and of expensive exascale applications in particular.