Convergence Analysis of the Hessian Estimation Evolution Strategy
This provides theoretical foundations for a class of optimization algorithms, which is incremental as it builds on existing HE-ES methods.
The paper tackles the problem of proving formal guarantees for Hessian Estimation Evolution Strategies (HE-ESs), specifically showing stability of the covariance matrix update and linear convergence on convex quadratic problems with a rate independent of the problem instance.
The class of algorithms called Hessian Estimation Evolution Strategies (HE-ESs) update the covariance matrix of their sampling distribution by directly estimating the curvature of the objective function. The approach is practically efficient, as attested by respectable performance on the BBOB testbed, even on rather irregular functions. In this paper we formally prove two strong guarantees for the (1+4)-HE-ES, a minimal elitist member of the family: stability of the covariance matrix update, and as a consequence, linear convergence on all convex quadratic problems at a rate that is independent of the problem instance.