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[2502.01594] Faster Adaptive Optimization via Expected Gradient Outer Product Reparameterization
Summary
This article presents a novel reparameterization method for adaptive optimization algorithms, enhancing their convergence properties through the expected gradient outer product (EGOP) matrix.
Why It Matters
Adaptive optimization algorithms are crucial in machine learning and signal processing. Understanding how to improve their performance through reparameterization can lead to more efficient training and better results in various applications, making this research significant for practitioners and researchers alike.
Key Takeaways
- Introduces a reparameterization method based on the expected gradient outer product (EGOP).
- Demonstrates that the choice of basis significantly affects the convergence of adaptive optimization algorithms.
- Provides theoretical and empirical evidence supporting the effectiveness of the EGOP matrix.
- Highlights the influence of EGOP spectral decay on algorithm performance in natural data scenarios.
- Encourages further exploration of basis transformations in adaptive optimization.
Computer Science > Machine Learning arXiv:2502.01594 (cs) [Submitted on 3 Feb 2025 (v1), last revised 13 Feb 2026 (this version, v2)] Title:Faster Adaptive Optimization via Expected Gradient Outer Product Reparameterization Authors:Adela DePavia, Jose Cruzado, Jiayou Liang, Vasileios Charisopoulos, Rebecca Willett View a PDF of the paper titled Faster Adaptive Optimization via Expected Gradient Outer Product Reparameterization, by Adela DePavia and 4 other authors View PDF HTML (experimental) Abstract:Adaptive optimization algorithms -- such as Adagrad, Adam, and their variants -- have found widespread use in machine learning, signal processing and many other settings. Several methods in this family are not rotationally equivariant, meaning that simple reparameterizations (i.e. change of basis) can drastically affect their convergence. However, their sensitivity to the choice of parameterization has not been systematically studied; it is not clear how to identify a "favorable" change of basis in which these methods perform best. In this paper we propose a reparameterization method and demonstrate both theoretically and empirically its potential to improve their convergence behavior. Our method is an orthonormal transformation based on the expected gradient outer product (EGOP) matrix, which can be approximated using either full-batch or stochastic gradient oracles. We show that for a broad class of functions, the sensitivity of adaptive algorithms to choice-of-basis is inf...
