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arXiv · 2310.14963

Studying K-FAC Heuristics by Viewing Adam through a Second-Order Lens

Ross M. Clarke·José Miguel Hernández-Lobato
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Abstract

Research into optimisation for deep learning is characterised by a tension between the computational efficiency of first-order, gradient-based methods (such as SGD and Adam) and the theoretical efficiency of second-order, curvature-based methods (such as quasi-Newton methods and K-FAC). Noting that second-order methods often only function effectively with the addition of stabilising heuristics (such as Levenberg-Marquardt damping), we ask how much these (as opposed to the second-order curvature model) contribute to second-order algorithms' performance. We thus study AdamQLR: an optimiser combining damping and learning rate selection techniques from K-FAC (Martens & Grosse, 2015) with the update directions proposed by Adam, inspired by considering Adam through a second-order lens. We evaluate AdamQLR on a range of regression and classification tasks at various scales and hyperparameter tuning methodologies, concluding K-FAC's adaptive heuristics are of variable standalone general effectiveness, and finding an untuned AdamQLR setting can achieve comparable performance vs runtime to tuned benchmarks.

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Ross M. Clarke, José Miguel Hernández-Lobato. 2024-06-13. Studying K-FAC Heuristics by Viewing Adam through a Second-Order Lens. https://arxiv.org/abs/2310.14963

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