  We study the theoretical capacity to statistically learn local landscape
information by Evolution Strategies (ESs). Specifically, we investigate the
covariance matrix when constructed by ESs operating with the selection operator
alone. We model continuous generation of candidate solutions about quadratic
basins of attraction, with deterministic selection of the decision vectors that
minimize the objective function values. Our goal is to rigorously show that
accumulation of winning individuals carries the potential to reveal valuable
information about the search landscape, e.g., as already practically utilized
by derandomized ES variants. We first show that the statistically-constructed
covariance matrix over such winning decision vectors shares the same
eigenvectors with the Hessian matrix about the optimum. We then provide an
analytic approximation of this covariance matrix for a non-elitist multi-child
$(1,\lambda)$-strategy, which holds for a large population size $\lambda$.
Finally, we also numerically corroborate our results.
