Geodesic
Asymptotic Analysis of the Ruppert – Polyak Averaging for Stochastic Order Oracle
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 5, pp. 961-978

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Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function’s internal mechanisms. One promising approach to addressing 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.
Keywords: stochastic order oracle, stochastic optimization, asymptotic convergence analysis 
@article{ND_2024_20_5_a15,
     author = {V. N. Smirnov and K. M. Kazistova and I. A. Sudakov and V. Leplat and A. V. Gasnikov and A. V. Lobanov},
     title = {Asymptotic {Analysis} of the {Ruppert} {\textendash} {Polyak} {Averaging} for {Stochastic} {Order} {Oracle}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {961--978},
     publisher = {mathdoc},
     volume = {20},
     number = {5},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2024_20_5_a15/}
}
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V. N. Smirnov; K. M. Kazistova; I. A. Sudakov; V. Leplat; A. V. Gasnikov; A. V. Lobanov. Asymptotic Analysis of the Ruppert – Polyak Averaging for Stochastic Order Oracle. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 5, pp. 961-978. http://geodesic.mathdoc.fr/item/ND_2024_20_5_a15/