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arXiv · 2203.02140

Whiplash Gradient Descent Dynamics

Subhransu S. Bhattacharjee·Ian R. Petersen
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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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Subhransu S. Bhattacharjee, Ian R. Petersen. 2022-03-04. Whiplash Gradient Descent Dynamics. https://arxiv.org/abs/2203.02140

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