Search for: All records

With a principled representation of uncertainty and closed form posterior updates, Gaussian processes (GPs) are a natural choice for online decision making. However, Gaussian processes typically require at least O(n2) computations for n training points, limiting their general applicability. Stochastic variational Gaussian processes (SVGPs) can provide scalable inference for a dataset of fixed size, but are difficult to efficiently condition on new data. We propose online variational conditioning (OVC), a procedure for efficiently conditioning SVGPs in an online setting that does not require re-training through the evidence lower bound with the addition of new data. OVC enables the pairing of SVGPs with advanced look-ahead acquisition functions for black-box optimization, even with non-Gaussian likelihoods. We show OVC provides compelling performance in a range of applications including active learning of malaria incidence, and reinforcement learning on MuJoCo simulated robotic control tasks. 

Bayesian optimization is a sample-efficient black-box optimization procedure that is typically applied to a small number of independent objectives. However, in practice we often wish to optimize objectives defined over many correlated outcomes (or “tasks”). For example, scientists may want to optimize the coverage of a cell tower network across a dense grid of locations. Similarly, engineers may seek to balance the performance of a robot across dozens of different environments via constrained or robust optimization. However, the Gaussian Process (GP) models typically used as probabilistic surrogates for multi-task Bayesian optimization scale poorly with the number of outcomes, greatly limiting applicability. We devise an efficient technique for exact multi-task GP sampling that combines exploiting Kronecker structure in the covariance matrices with Matheron’s identity, allowing us to perform Bayesian optimization using exact multi-task GP models with tens of thousands of correlated outputs. In doing so, we achieve substantial improvements in sample efficiency compared to existing approaches that model solely the outcome metrics. We demonstrate how this unlocks a new class of applications for Bayesian optimization across a range of tasks in science and engineering, including optimizing interference patterns of an optical interferometer with 65,000 outputs. 

Nonlinear time history analyses were conducted for 5-story and 12-story prototype buildings that used post-tensioned cross-laminated timber rocking walls coupled with U-shaped flexural plates (UFPs) as the lateral force resisting system. The building models were subjected to 22 far-field and 28 near-fault ground motions, with and without directivity effects, scaled to the design earthquake and maximum considered earthquake for Seattle, with ASCE Site Class D. The buildings were designed to performance objectives that limited structural damage to crushing at the wall toes and nonlinear deformation in the UFPs, while ensuring code-based interstory drift requirements were satisfied and the post-tensioned rods remained linear. The walls of the 12-story building had a second rocking joint at midheight to reduce flexural demands in the lower stories and interstory drift in the upper stories. The interstory drift, in-plane wall shear and overturning moment, UFP deformation, and extent of wall toe crushing is summarized for each building. Near-fault ground motions with directivity effects resulted in the largest demands for the 5-story building, while the midheight rocking joint diminished the influence of ground motion directivity effects in the 12-story building. Results for both buildings confirmed that UFPs located higher from the base of the walls dissipated more energy compared to UFPs closer to the base. 

One of the most compelling features of Gaussian process (GP) regression is its ability to provide well-calibrated posterior distributions. Recent ad- vances in inducing point methods have sped up GP marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining computational bottlenecks. In this paper we address these shortcom- ings by using the Lanczos algorithm to rapidly ap- proximate the predictive covariance matrix. Our approach, which we refer to as LOVE (LanczOs Variance Estimates), substantially improves time and space complexity. In our experiments, LOVE computes covariances up to 2,000 times faster and draws samples 18,000 times faster than existing methods, all without sacrificing accuracy.