A Canonical Structure for Constructing Projected First-Order Algorithms With Delayed Feedback
This work provides a method for improving optimization algorithms in scenarios with delays, but it appears incremental as it builds on existing Lur'e representations and projection techniques.
The paper tackles the problem of extending unconstrained first-order optimization algorithms to set-constrained ones while handling delayed gradient feedback, achieving optimal solutions with preserved convergence rates.
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.