A Closed Loop Gradient Descent Algorithm applied to Rosenbrock's function

• URL: http://arxiv.org/abs/2108.12883v2
• Date: Tue, 31 Aug 2021 17:11:45 GMT
• Title: A Closed Loop Gradient Descent Algorithm applied to Rosenbrock's function
• Authors: Subhransu Bhattacharjee and Ian Petersen
• Abstract summary: We introduce a novel adaptive technique for an gradient system which finds application as a gradient descent algorithm for unconstrained inertial damping. Also using Lyapunov stability analysis, we demonstrate the performance of the continuous numerical-time version of the algorithm.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an improvement on existing momentum-based gradient optimisation methods. Also using Lyapunov stability analysis, we demonstrate the performance of the continuous-time version of the algorithm. Using numerical simulations, we consider the performance of its discrete-time counterpart obtained by using the symplectic Euler method of discretisation.

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