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Stochastic Adversarial Noise in the “Black Box” Optimization Problem

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Optimization and Applications (OPTIMA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14395))

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Abstract

This paper is devoted to the study of the solution of a stochastic convex black box optimization problem. Where the black box problem means that the gradient-free oracle only returns the value of objective function, not its gradient. We consider non-smooth and smooth setting of the solution to the black box problem under adversarial stochastic noise. For two techniques creating gradient-free methods: smoothing schemes via \(L_1\) and \(L_2\) randomizations, we find the maximum allowable level of adversarial stochastic noise that guarantees convergence. Finally, we analyze the convergence behavior of the algorithms under the condition of a large value of noise level.

The research was supported by Russian Science Foundation (project No. 21-71- 30005), https://rscf.ru/en/project/21-71-30005/.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Aleksandr Lobanov

  2. ISP RAS Research Center for Trusted Artificial Intelligence, Moscow, Russia

    Aleksandr Lobanov

  3. Moscow Aviation Institute, Moscow, Russia

    Aleksandr Lobanov

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  1. Aleksandr Lobanov
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Correspondence to Aleksandr Lobanov .

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Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Lobanov, A. (2023). Stochastic Adversarial Noise in the “Black Box” Optimization Problem. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2023. Lecture Notes in Computer Science, vol 14395. Springer, Cham. https://doi.org/10.1007/978-3-031-47859-8_5

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  • DOI: https://doi.org/10.1007/978-3-031-47859-8_5

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  • Print ISBN: 978-3-031-47858-1

  • Online ISBN: 978-3-031-47859-8

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