Principled Sample Set Construction in Noisy Environments: Insights from work on the Curvature Aligned Simplex Gradient
Abstract: The talk will focus on deriving a practical sample set selection method for the simplex gradient, based on the paper ‘Curvature Aligned Simplex Gradient: Principled Sample Set Construction for Numerical Differentiation’ [https://arxiv.org/pdf/2310.12712.pdf]. The motivation for exploring the simplex gradient stems from a desire to understand and utilize the information that can be obtained from noisy black-box systems. Specifically, we seek to understand how historical function evaluations may inform the selection of future sampling locations for use in optimization and interacting particle methods. To this end, we prove the optimality of our sample set for a mean squared error objective and demonstrate the effectiveness of fully utilizing curvature estimates to inform sample set construction. We present numerical results for applications in sensitivity analysis and derivative-free optimization.
Bio: Daniel Lengyel is a final-year PhD student at Imperial College London in the Department of Computing. His interests lie in adaptive sampling, derivative-free optimization, and interacting particle methods. Prior to his PhD, he obtained his Bachelor’s degrees in Mathematics and Computer Science at UC Berkeley, where he spent significant time at the RISELab working on model predictive control methods for HVAC systems as part of the XBOS-DR project.