О некоторых стохастических методах зеркального спуска для условных задач онлайн-оптимизации

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Список литературы:

  1. B. Awerbuch, R. Kleinberg. Online linear optimization and adaptive routing // Journal of Computer and System Sciences. — 2008. — V. 74, no. 1. — P. 97–114. — DOI: 10.1016/j.jcss.2007.04.016. — MathSciNet: MR2364184.
  2. A. Bayandina. Adaptive Stochastic Mirror Descent for Constrained Optimization. — 2017. — https://arxiv.org/pdf/1705.02031.pdf .
  3. A. Bayandina, A. Gasnikov, E. Gasnikova, S. Matsievsky. Primal-dual mirror descent for the stochastic programming problems with functional constraints // Computational Mathematics and Mathematical Physics. — 2018. — (accepted). — https://arxiv.org/pdf/1604.08194.pdf. — in Russian. — MathSciNet: MR3884238.
  4. A. Bayandina, P. Dvurechensky, A. Gasnikov, F. Stonyakin, A. Titov. Mirror descent and convex optimization problems with non-smooth inequality constraints / Large-Scale and Distributed Optimization. Lecture Notes in Mathematics. — 2018. — V. 2227. — P. 181–213. — MathSciNet: MR3888675.
  5. A. Beck, A. Ben-Tal, N. Guttmann-Beck, L. Tetruashvili. The comirror algorithm for solving nonsmooth constrained convex problems // Operations Research Letters. — 2010. — V. 38, no. 6. — P. 493–498. — DOI: 10.1016/j.orl.2010.08.005. — MathSciNet: MR2734206.
  6. A. Beck, M. Teboulle. Mirror descent and nonlinear projected subgradient methods for convex optimization // Operations Research Letters. — 2003. — V. 31, no. 3. — P. 167–175. — DOI: 10.1016/S0167-6377(02)00231-6. — MathSciNet: MR1967286.
  7. A. Ben-Tal, A. Nemirovski. Lectures on Modern Convex Optimization. — Philadelphia: Society for Industrial and Applied Mathematics, 2001. — 590 p. — MathSciNet: MR1857264.
  8. A. Ben-Tal, A. Nemirovski. Robust Truss Topology Design via semidefinite programming // SIAM Journal on Optimization. — 1997. — V. 7, no. 4. — P. 991–1016. — DOI: 10.1137/S1052623495291951. — MathSciNet: MR1479611.
  9. S. Boyd, L. Vandenberghe. Convex Optimization. — New York: Cambridge University Press, 2004. — 730 p. — MathSciNet: MR2061575.
  10. S. Bubeck, R. Eldan. Multi-scale exploration of convex functions and bandit convex optimization. — 2015. — e-print. — http://research.microsoft.com/en-us/um/people/sebubeck/ConvexBandits.pdf.
  11. S. Bubeck, N. Cesa-Bianchi. Regret analysis of stochastic and nonstochastic multi-armed bandit problems // Foundation and Trends in Machine Learning. — 2012. — V. 5, no. 1. — P. 1–122. — DOI: 10.1561/2200000024.
  12. A. V. Gasnikov, A. A. Lagunovskaya, L. E. Morozova. On the relationship between simulation logit dynamics in the population game theory and a mirror descent method in the online optimization using the example of the shortest path problem // PROCEEDINGS OF MIPT. — 2015. — V. 7, no. 4. — P. 104–113. — in Russian.
  13. A. V. Gasnikov, A. A. Lagunovskaya, I. N. Usmanova, F. A. Fedorenko, E. A. Krymova. Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and stronglyconvex case // Automation and Remote Control. — 2017. — V. 78, no. 2. — P. 224–234. — DOI: 10.1134/S0005117917020035. — MathSciNet: MR3665422.
  14. E. Hazan, S. Kale. Beyond the regret minimization barrier: Optimal algorithms for stochastic stronglyconvex optimization // JMLR. — 2014. — V. 15. — P. 2489–2512. — MathSciNet: MR3247148.
  15. E. Hazan. Introduction to online convex optimization // Foundations and Trends in Optimization. — 2015. — V. 2, no. 3–4. — P. 157–325.
  16. Hao Yu, Neely M. J., Wei. Xiaohan. Online Convex Optimization with Stochastic Constraints. — 2017. — https://arxiv.org/pdf/1708.03741.pdf .
  17. R. Jenatton, J. Huang, C. Archambeau. Adaptive Algorithms for Online Convex Optimization with Long-term Constraints. — 2015. — https://arxiv.org/abs/1512.07422 .
  18. A. Kalai, S. Vempala. Efficient algorithms for online decision problems // Journal of Computer and System Sciences. — 2005. — V. 71. — P. 291–307. — DOI: 10.1016/j.jcss.2004.10.016. — MathSciNet: MR2168355.
  19. G. Lugosi, N. Cesa-Bianchi. Prediction, learning and games. — New York: Cambridge University Press, 2006. — 403 p. — MathSciNet: MR2409394.
  20. A. Nemirovski. Efficient methods for large-scale convex optimization problems // Ekonomika i Matematicheskie Metody. — 1979. — V. 15, no. 1. — in Russian.
  21. A. Nemirovsky, D. Yudin. Problem Complexity and Method Efficiency in Optimization. — New York: J. Wiley & Sons, 1983. — 404 p. — MathSciNet: MR0702836.
  22. Yu. Nesterov. Introductory Lectures on Convex Optimization: A Basic Course. — Massachusetts: Kluwer Academic Publishers, 2004. — 236 p. — MathSciNet: MR2142598.
  23. B. Polyak. A general method of solving extremum problems // Soviet Mathematics Doklady. — 1967. — V. 8, no. 3. — P. 593–597. — in Russian. — MathSciNet: MR0217997.
  24. N. Z. Shor. Generalized gradient descent with application to block programming // Kibernetika. — 1967. — V. 3, no. 3. — P. 53–55. — in Russian.
  25. F. S. Stonyakin, M. S. Alkousa, A. N. Stepanov, M. A. Barinov. Adaptive mirror descent algorithms in convex programming problems with Lipschitz constraints // Trudy Instituta Matematiki i Mekhaniki URO RAN. — 2018. — V. 24, no. 2. — P. 266–279. — DOI: 10.21538/0134-4889-2018-24-2-266-279. — Math-Net: Mi eng/timm1541. — MathSciNet: MR3853340.
  26. S. Shpirko, Yu. Nesterov. Primal-dual subgradient methods for huge-scale linear conic problem // SIAM Journal on Optimization. — 2014. — V. 24, no. 3. — P. 1444–1457. — DOI: 10.1137/130929345. — MathSciNet: MR3257645.
  27. A. A. Titov, F. S. Stonyakin, A. V. Gasnikov, M. S. Alkousa. Mirror Descent and Constrained Online Optimization Problems // Communications in Computer and Information Science. — 2019. — V. 974. — P. 64–78. — Optimization and Applications. 9th International Conference OPTIMA- 2018 (Petrovac, Montenegro, October 1–5, 2018). Revised Selected Papers. — DOI: 10.1007/978-3-030-10934-9_5.
  28. M. Zinkevich. Online Convex Programming and Generalized Infinitesimal Gradient Ascent / Proceedings of International Conference on Machine Learning (ICML). — 2003.

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