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arXiv · 2604.02762

A Canonical Structure for Constructing Projected First-Order Algorithms With Delayed Feedback

Mengmou Li·Yu Zhou·Xun Shen·Masaaki Nagahara
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Abstract

This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback. The proposed canonical structure is obtained through a simple linear transformation. It enables a direct extension from unconstrained optimization algorithms to set-constrained ones through projection in a Lyapunov-induced norm. The resulting projected algorithms attain the optimal solution while preserving the convergence rates of their unconstrained counterparts.

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Mengmou Li, Yu Zhou, Xun Shen, Masaaki Nagahara. 2026-04-03. A Canonical Structure for Constructing Projected First-Order Algorithms With Delayed Feedback. https://arxiv.org/abs/2604.02762

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