Scalable Derivative-Free Optimization for Nonlinear Least-Squares Problems

Coralia Cartis; Tyler Ferguson; Lindon Roberts

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arXiv · 2007.13243

Scalable Derivative-Free Optimization for Nonlinear Least-Squares Problems

Coralia Cartis·Tyler Ferguson·Lindon Roberts

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Abstract

Derivative-free - or zeroth-order - optimization (DFO) has gained recent attention for its ability to solve problems in a variety of application areas, including machine learning, particularly involving objectives which are stochastic and/or expensive to compute. In this work, we develop a novel model-based DFO method for solving nonlinear least-squares problems. We improve on state-of-the-art DFO by performing dimensionality reduction in the observational space using sketching methods, avoiding the construction of a full local model. Our approach has a per-iteration computational cost which is linear in problem dimension in a big data regime, and numerical evidence demonstrates that, compared to existing software, it has dramatically improved runtime performance on overdetermined least-squares problems.

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Coralia Cartis, Tyler Ferguson, Lindon Roberts. 2020-07-26. Scalable Derivative-Free Optimization for Nonlinear Least-Squares Problems. https://arxiv.org/abs/2007.13243

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