Whiplash Gradient Descent Dynamics

• URL: http://arxiv.org/abs/2203.02140v4
• Date: Mon, 19 Jun 2023 12:13:50 GMT
• Title: Whiplash Gradient Descent Dynamics
• Authors: Subhransu S. Bhattacharjee and Ian R. Petersen
• Abstract summary: We introduce the symplectic convergence analysis for the Whiplash system for convex functions. We study the algorithm's performance for various costs and provide a practical methodology for analyzing convergence rates.
• Score: 2.0508733018954843
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: In this paper, we propose the Whiplash Inertial Gradient dynamics, a closed-loop optimization method that utilises gradient information, to find the minima of a cost function in finite-dimensional settings. We introduce the symplectic asymptotic convergence analysis for the Whiplash system for convex functions. We also introduce relaxation sequences to explain the non-classical nature of the algorithm and an exploring heuristic variant of the Whiplash algorithm to escape saddle points, deterministically. We study the algorithm's performance for various costs and provide a practical methodology for analyzing convergence rates using integral constraint bounds and a novel Lyapunov rate method. Our results demonstrate polynomial and exponential rates of convergence for quadratic cost functions.

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