Ruppert-Polyak averaging for Stochastic Order Oracle
This work provides an incremental improvement for researchers in black-box optimization by enhancing the theoretical understanding of convergence rates.
The paper tackles the problem of improving the asymptotic convergence rate estimation for the Stochastic Order Oracle concept in black-box optimization, achieving a more accurate covariance matrix estimation validated by numerical experiments.
Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, similar to other Order Oracle Concepts, relies solely on relative comparisons of function values without requiring access to the exact values. This paper presents a novel, improved estimation of the covariance matrix for the asymptotic convergence of the Stochastic Order Oracle Concept. Our work surpasses existing research in this domain by offering a more accurate estimation of asymptotic convergence rate. Finally, numerical experiments validate our theoretical findings, providing strong empirical support for our proposed approach.