Additive Drift as an Optimization Problem for the (1 + 1)-ES
Year: 2025
Type: conference-paper
Abstract: We present a novel method for constructing a close-to-optimal potential function for drift analysis of evolution strategies and other numerical optimization algorithms. It is based on a piecewise linear ansatz for the potential function, defined by potential values on a discrete grid of states together with a corresponding interpolation scheme. We compute or approximate the algorithm dynamics on the grid and then construct a linear program from expected progress and (weighted) state transitions. The solution of the optimization problem gives rise to parameters of the potential function maximizing (additive) drift. Under mild assumptions, the proceeding yields an arbitrarily close approximation of the optimal potential function at the expense of growing computational demands. As a proof of concept we apply the method to the (1+1) evolution strategy on the two-dimensional sphere function.
Authors: Alexander Jungeilges, Tobias Glasmachers
Institution: Ruhr University Bochum
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4413311664