Xiaoye S. Li

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, Xiaoye S. Li, Yang Liu et al.

Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to optimistically narrow posterior intervals and biased decisions. We study GP regression under input measurement uncertainty by representing each noisy input as a probability measure and defining covariance through Wasserstein distances between these measures. Building on this perspective, we instantiate a deterministic projected Wasserstein ARD (PWA) kernel whose one-dimensional components admit closed-form expressions and whose product structure yields a scalable, positive-definite kernel on distributions. Unlike latent-input GP models, PWA-based GPs (\PWAGPs) handle input noise without introducing unobserved covariates or Monte Carlo projections, making uncertainty quantification more transparent and robust.

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.

Hongyuan Zhan, Gabriel Gomes, Xiaoye S. Li et al.

Computational efficiency is an important consideration for deploying machine learning models for time series prediction in an online setting. Machine learning algorithms adjust model parameters automatically based on the data, but often require users to set additional parameters, known as hyperparameters. Hyperparameters can significantly impact prediction accuracy. Traffic measurements, typically collected online by sensors, are serially correlated. Moreover, the data distribution may change gradually. A typical adaptation strategy is periodically re-tuning the model hyperparameters, at the cost of computational burden. In this work, we present an efficient and principled online hyperparameter optimization algorithm for Kernel Ridge regression applied to traffic prediction problems. In tests with real traffic measurement data, our approach requires as little as one-seventh of the computation time of other tuning methods, while achieving better or similar prediction accuracy.