A. V. Gasnikov, E. A. Krymova, A. A. Lagunovskaya, I. N. Usmanova, F. A. Fedorenko, “Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case”, Avtomat. i Telemekh., 2017, no. 2, 36–49; Autom. Remote Control, 78:2 (2017), 224

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Avtomatika i Telemekhanika, 2017, Issue 2, Pages 36–49 (Mi at14682)

This article is cited in 37 scientific papers (total in 37 papers)

Stochastic Systems, Queuing Systems

Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case

A. V. Gasnikov^ab, E. A. Krymova^b, A. A. Lagunovskaya^ca, I. N. Usmanova^ab, F. A. Fedorenko^a

^a Moscow Institute of Physics and Technology (State University), Moscow, Russia
^b Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia
^c Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

Full-text PDF (673 kB) Citations (37)

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Abstract: In this paper the gradient-free modification of the mirror descent method for convex stochastic online optimization problems is proposed. The crucial assumption in the problem setting is that function realizations are observed with minor noises. The aim of this paper is to derive the convergence rate of the proposed methods and to determine a noise level which does not significantly affect the convergence rate.

Keywords: online optimization, gradient-free, inexact oracle, stochastic optimization.

Funding agency	Grant number
Russian Foundation for Basic Research	15-31-20571 мол_а_вед
Russian Science Foundation	14-50-00150
This work was supported by the Russian Foundation for Basic Research, project no. 15-31-20571 mol_a_ved. The work of the first two authors was partially supported by the Russian Science Foundation, project no. 14-50-00150 in Institute for Information Transmission Problems of the Russian Academy of Sciences.

Presented by the member of Editorial Board: P. S. Shcherbakov

Received: 16.10.2014

English version:
Automation and Remote Control, 2017, Volume 78, Issue 2, Pages 224–234
DOI: https://doi.org/10.1134/S0005117917020035

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. V. Gasnikov, E. A. Krymova, A. A. Lagunovskaya, I. N. Usmanova, F. A. Fedorenko, “Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case”, Avtomat. i Telemekh., 2017, no. 2, 36–49; Autom. Remote Control, 78:2 (2017), 224–234

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/at14682

https://www.mathnet.ru/eng/at/y2017/i2/p36

This publication is cited in the following 37 articles:

Yuanhanqing Huang, Jianghai Hu, “Zeroth-Order Learning in Continuous Games via Residual Pseudogradient Estimates”, IEEE Trans. Automat. Contr., 70:4 (2025), 2258
Yan Zhang, Michael M. Zavlanos, “Cooperative Multiagent Reinforcement Learning With Partial Observations”, IEEE Trans. Automat. Contr., 69:2 (2024), 968
A. V. Gasnikov, A. V. Lobanov, F. S. Stonyakin, “Highly Smooth Zeroth-Order Methods for Solving Optimization Problems under the PL Condition”, Comput. Math. and Math. Phys., 64:4 (2024), 739
Wouter Jongeneel, Man-Chung Yue, Daniel Kuhn, “Small Errors in Random Zeroth-Order Optimization Are Imaginary”, SIAM J. Optim., 34:3 (2024), 2638
Alexander Gasnikov, Darina Dvinskikh, Pavel Dvurechensky, Eduard Gorbunov, Aleksandr Beznosikov, Alexander Lobanov, Encyclopedia of Optimization, 2024, 1
Yan Zhang, Yi Zhou, Kaiyi Ji, Yi Shen, Michael M. Zavlanos, “Boosting One-Point Derivative-Free Online Optimization via Residual Feedback”, IEEE Trans. Automat. Contr., 69:9 (2024), 6309
Andrey Veprikov, Alexander Bogdanov, Vladislav Minashkin, Aleksandr Beznosikov, “New aspects of black box conditional gradient: Variance reduction and one point feedback”, Chaos, Solitons & Fractals, 189 (2024), 115654
G. K. Bychkov, D. M. Dvinskikh, A. V. Antsiferova, A. V. Gasnikov, A. V. Lobanov, “Accelerated Zero-Order SGD under High-Order Smoothness and Overparameterized Regime”, Rus. J. Nonlin. Dyn., 20:5 (2024), 759–788
Pavel Dvurechensky, Alexander Gasnikov, Alexander Tyurin, Vladimir Zholobov, Springer Proceedings in Mathematics & Statistics, 425, Foundations of Modern Statistics, 2023, 511
B. A. Alashkar, A. V. Gasnikov, D. M. Dvinskikh, A. V. Lobanov, “Gradient-free federated learning methods with $l_1$ and $l_2$ -randomization for non-smooth convex stochastic optimization problems”, Comput. Math. Math. Phys., 63:9 (2023), 1600–1653
Oleg Savchuk, Fedor Stonyakin, Mohammad Alkousa, Rida Zabirova, Alexander Titov, Alexander Gasnikov, Communications in Computer and Information Science, 1881, Mathematical Optimization Theory and Operations Research: Recent Trends, 2023, 29
Aleksandr Lobanov, Andrew Veprikov, Georgiy Konin, Aleksandr Beznosikov, Alexander Gasnikov, Dmitry Kovalev, “Non-smooth setting of stochastic decentralized convex optimization problem over time-varying Graphs”, Comput Manag Sci, 20:1 (2023)
Aleksandr Lobanov, Lecture Notes in Computer Science, 14395, Optimization and Applications, 2023, 60
Nikita Kornilov, Alexander Gasnikov, Pavel Dvurechensky, Darina Dvinskikh, “Gradient-free methods for non-smooth convex stochastic optimization with heavy-tailed noise on convex compact”, Comput Manag Sci, 20:1 (2023)
Raghu Bollapragada, Stefan M. Wild, “Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization”, Math. Prog. Comp., 15:2 (2023), 327
Balasubramanian K., Ghadimi S., “Zeroth-Order Nonconvex Stochastic Optimization: Handling Constraints, High Dimensionality, and Saddle Points”, Found. Comput. Math., 22:1 (2022), 35–76
A. I. Bazarova, A. N. Beznosikov, A. V. Gasnikov, “Linearly convergent gradient-free methods for minimization of parabolic approximation”, Kompyuternye issledovaniya i modelirovanie, 14:2 (2022), 239–255
Abhishek Roy, Lingqing Shen, Krishnakumar Balasubramanian, Saeed Ghadimi, “Stochastic zeroth-order discretizations of Langevin diffusions for Bayesian inference”, Bernoulli, 28:3 (2022)
Vasilii Novitskii, Alexander Gasnikov, “Improved exploitation of higher order smoothness in derivative-free optimization”, Optim Lett, 16:7 (2022), 2059
Darina Dvinskikh, Vladislav Tominin, Iaroslav Tominin, Alexander Gasnikov, Lecture Notes in Computer Science, 13367, Mathematical Optimization Theory and Operations Research, 2022, 18

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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