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Journal articles on the topic 'Descente en mirroir'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Duchi, John C., Alekh Agarwal, Mikael Johansson, and Michael I. Jordan. "Ergodic Mirror Descent." SIAM Journal on Optimization 22, no. 4 (2012): 1549–78. http://dx.doi.org/10.1137/110836043.

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2

Lei, Yunwen, and Ding-Xuan Zhou. "Convergence of online mirror descent." Applied and Computational Harmonic Analysis 48, no. 1 (2020): 343–73. http://dx.doi.org/10.1016/j.acha.2018.05.005.

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3

Chen, Po-An, and Chi-Jen Lu. "Generalized mirror descents in congestion games." Artificial Intelligence 241 (December 2016): 217–43. http://dx.doi.org/10.1016/j.artint.2016.09.002.

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4

Lei, Yunwen, and Ding-Xuan Zhou. "Analysis of Online Composite Mirror Descent Algorithm." Neural Computation 29, no. 3 (2017): 825–60. http://dx.doi.org/10.1162/neco_a_00930.

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We study the convergence of the online composite mirror descent algorithm, which involves a mirror map to reflect the geometry of the data and a convex objective function consisting of a loss and a regularizer possibly inducing sparsity. Our error analysis provides convergence rates in terms of properties of the strongly convex differentiable mirror map and the objective function. For a class of objective functions with Hölder continuous gradients, the convergence rates of the excess (regularized) risk under polynomially decaying step sizes have the order [Formula: see text] after [Formula: se

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5

Miyashita, Megumi, Shiro Yano, and Toshiyuki Kondo. "Mirror descent search and its acceleration." Robotics and Autonomous Systems 106 (August 2018): 107–16. http://dx.doi.org/10.1016/j.robot.2018.04.009.

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6

Raskutti, Garvesh, and Sayan Mukherjee. "The Information Geometry of Mirror Descent." IEEE Transactions on Information Theory 61, no. 3 (2015): 1451–57. http://dx.doi.org/10.1109/tit.2015.2388583.

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7

Yu, Yue, and Behcet Acikmese. "RLC Circuits-Based Distributed Mirror Descent Method." IEEE Control Systems Letters 4, no. 3 (2020): 548–53. http://dx.doi.org/10.1109/lcsys.2020.2972908.

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8

Hanzely, Filip, and Peter Richtárik. "Fastest rates for stochastic mirror descent methods." Computational Optimization and Applications 79, no. 3 (2021): 717–66. http://dx.doi.org/10.1007/s10589-021-00284-5.

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9

Wei, Xiaohan, Hao Yu, and Michael J. Neely. "Online Primal-Dual Mirror Descent under Stochastic Constraints." ACM SIGMETRICS Performance Evaluation Review 48, no. 1 (2020): 3–4. http://dx.doi.org/10.1145/3410048.3410051.

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10

Wei, Xiaohan, Hao Yu, and Michael J. Neely. "Online Primal-Dual Mirror Descent under Stochastic Constraints." Proceedings of the ACM on Measurement and Analysis of Computing Systems 4, no. 2 (2020): 1–36. http://dx.doi.org/10.1145/3392157.

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11

Doan, Thinh T., Subhonmesh Bose, D. Hoa Nguyen, and Carolyn L. Beck. "Convergence of the Iterates in Mirror Descent Methods." IEEE Control Systems Letters 3, no. 1 (2019): 114–19. http://dx.doi.org/10.1109/lcsys.2018.2854889.

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12

Lan, Guanghui, Arkadi Nemirovski, and Alexander Shapiro. "Validation analysis of mirror descent stochastic approximation method." Mathematical Programming 134, no. 2 (2011): 425–58. http://dx.doi.org/10.1007/s10107-011-0442-6.

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13

Wang, Yinghui, Zhipeng Tu, and Huashu Qin. "Distributed stochastic mirror descent algorithm for resource allocation problem." Control Theory and Technology 18, no. 4 (2020): 339–47. http://dx.doi.org/10.1007/s11768-020-00018-8.

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14

Shahrampour, Shahin, and Ali Jadbabaie. "Distributed Online Optimization in Dynamic Environments Using Mirror Descent." IEEE Transactions on Automatic Control 63, no. 3 (2018): 714–25. http://dx.doi.org/10.1109/tac.2017.2743462.

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15

SAHU, O. P., M. K. SONI, and I. M. TALWAR. "DESIGNING QUADRATURE MIRROR FILTER BANKS USING STEEPEST DESCENT METHOD." Journal of Circuits, Systems and Computers 15, no. 01 (2006): 29–41. http://dx.doi.org/10.1142/s0218126606002903.

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This paper proposes a new technique for the design of quadrature mirror filter (QMF) banks by exploiting steepest descent method. The design problem is formulated to minimize an objective function, which is a weighted sum of the pass band error and stop band residual energy of the low pass analysis filter of the QMF bank. The minimization has been carried out gradually by respective optimum step lengths in the corresponding steepest descent directions of a linear combination of the objective function and square of the reconstruction error of the QMF bank at the quadrature frequency by optimizi

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16

Nedić, Angelia, and Soomin Lee. "On Stochastic Subgradient Mirror-Descent Algorithm with Weighted Averaging." SIAM Journal on Optimization 24, no. 1 (2014): 84–107. http://dx.doi.org/10.1137/120894464.

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17

Halder, Abhishek. "DeGroot–Friedkin Map in Opinion Dynamics Is Mirror Descent." IEEE Control Systems Letters 3, no. 2 (2019): 463–68. http://dx.doi.org/10.1109/lcsys.2019.2900452.

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18

Yuan, Deming, Yiguang Hong, Daniel W. C. Ho, and Guoping Jiang. "Optimal distributed stochastic mirror descent for strongly convex optimization." Automatica 90 (April 2018): 196–203. http://dx.doi.org/10.1016/j.automatica.2017.12.053.

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19

Li, Jueyou, Guoquan Li, Zhiyou Wu, and Changzhi Wu. "Stochastic mirror descent method for distributed multi-agent optimization." Optimization Letters 12, no. 6 (2016): 1179–97. http://dx.doi.org/10.1007/s11590-016-1071-z.

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20

Ivanova, Anastasiya, Fedor Stonyakin, Dmitry Pasechnyuk, Evgeniya Vorontsova, and Alexander Gasnikov. "Adaptive Mirror Descent for the Network Utility Maximization Problem." IFAC-PapersOnLine 53, no. 2 (2020): 7851–56. http://dx.doi.org/10.1016/j.ifacol.2020.12.1958.

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21

Miyashita, Megumi, Toshiyuki Kondo, and Shiro Yano. "Reinforcement learning with constraint based on mirror descent algorithm." Results in Control and Optimization 4 (September 2021): 100048. http://dx.doi.org/10.1016/j.rico.2021.100048.

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22

Han Xingzi, 韩杏子, 俞信 Yu Xin, and 董冰 Dong Bing. "Using Stochastic Parallel Gradient Descent Control Algorithm to Calibrate Sencond Mirror in Three-Mirror System." Laser & Optoelectronics Progress 47, no. 4 (2010): 042201. http://dx.doi.org/10.3788/lop47.042201.

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23

Luong, Duy V. N., Panos Parpas, Daniel Rueckert, and Berç Rustem. "A Weighted Mirror Descent Algorithm for Nonsmooth Convex Optimization Problem." Journal of Optimization Theory and Applications 170, no. 3 (2016): 900–915. http://dx.doi.org/10.1007/s10957-016-0963-5.

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24

Beck, Amir, and Marc Teboulle. "Mirror descent and nonlinear projected subgradient methods for convex optimization." Operations Research Letters 31, no. 3 (2003): 167–75. http://dx.doi.org/10.1016/s0167-6377(02)00231-6.

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25

Li, Jueyou, Guo Chen, Zhaoyang Dong, and Zhiyou Wu. "Distributed mirror descent method for multi-agent optimization with delay." Neurocomputing 177 (February 2016): 643–50. http://dx.doi.org/10.1016/j.neucom.2015.12.017.

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26

Nazin, A. V., and A. A. Tremba. "Saddle point mirror descent algorithm for the robust PageRank problem." Automation and Remote Control 77, no. 8 (2016): 1403–18. http://dx.doi.org/10.1134/s0005117916080075.

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27

Bayandina, A. S., A. V. Gasnikov, E. V. Gasnikova, and S. V. Matsievskii. "Primal–Dual Mirror Descent Method for Constraint Stochastic Optimization Problems." Computational Mathematics and Mathematical Physics 58, no. 11 (2018): 1728–36. http://dx.doi.org/10.1134/s0965542518110039.

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28

Dang, Cong D., and Guanghui Lan. "Stochastic Block Mirror Descent Methods for Nonsmooth and Stochastic Optimization." SIAM Journal on Optimization 25, no. 2 (2015): 856–81. http://dx.doi.org/10.1137/130936361.

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29

Zhou, Zhengyuan, Panayotis Mertikopoulos, Nicholas Bambos, Stephen P. Boyd, and Peter W. Glynn. "On the Convergence of Mirror Descent beyond Stochastic Convex Programming." SIAM Journal on Optimization 30, no. 1 (2020): 687–716. http://dx.doi.org/10.1137/17m1134925.

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30

Nazin, A. V., A. S. Nemirovsky, A. B. Tsybakov, and A. B. Juditsky. "Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method." Automation and Remote Control 80, no. 9 (2019): 1607–27. http://dx.doi.org/10.1134/s0005117919090042.

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31

Nazin, A. V. "Search for a saddle point of a convex-concave stochastic game by the adaptive method of mirror descent." Transaction Kola Science Centre 11, no. 8-2020 (2020): 182–84. http://dx.doi.org/10.37614/2307-5252.2020.8.11.025.

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A stochastic game problem of 2 persons with a zero sum is considered, leading to the search for a saddle point of the game function based on the gradient approach. We study mirror descent algorithms, both adaptive and non-adaptive. The main results are proved. An illustrative example is discussed.

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32

Boffi, Nicholas M., and Jean-Jacques E. Slotine. "Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction." Neural Computation 33, no. 3 (2021): 590–673. http://dx.doi.org/10.1162/neco_a_01360.

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Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization and machine learning, we show that there exists considerable untapped potential in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction. We begin by i

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33

Alkousa, Mohammad S. "On some stochastic mirror descent methods for constrained online optimization problems." Computer Research and Modeling 11, no. 2 (2019): 205–17. http://dx.doi.org/10.20537/2076-7633-2019-11-2-205-217.

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34

Hien, Le Thi Khanh, Cuong V. Nguyen, Huan Xu, Canyi Lu, and Jiashi Feng. "Accelerated Randomized Mirror Descent Algorithms for Composite Non-strongly Convex Optimization." Journal of Optimization Theory and Applications 181, no. 2 (2019): 541–66. http://dx.doi.org/10.1007/s10957-018-01469-5.

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35

Mertikopoulos, Panayotis, and Mathias Staudigl. "Stochastic Mirror Descent Dynamics and Their Convergence in Monotone Variational Inequalities." Journal of Optimization Theory and Applications 179, no. 3 (2018): 838–67. http://dx.doi.org/10.1007/s10957-018-1346-x.

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36

Li, Jueyou, Guo Chen, Zhaoyang Dong, Zhiyou Wu, and Minghai Yao. "Distributed mirror descent method for saddle point problems over directed graphs." Complexity 21, S2 (2016): 178–90. http://dx.doi.org/10.1002/cplx.21794.

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37

Ben-Tal, Aharon, Tamar Margalit, and Arkadi Nemirovski. "The Ordered Subsets Mirror Descent Optimization Method with Applications to Tomography." SIAM Journal on Optimization 12, no. 1 (2001): 79–108. http://dx.doi.org/10.1137/s1052623499354564.

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38

Shiyan, D. N., and A. V. Kolnogorov. "Simulation of the mirror descent algorithm on distributions with different variances." Journal of Physics: Conference Series 1658 (October 2020): 012051. http://dx.doi.org/10.1088/1742-6596/1658/1/012051.

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39

Nazin, A. V. "Algorithms of Inertial Mirror Descent in Convex Problems of Stochastic Optimization." Automation and Remote Control 79, no. 1 (2018): 78–88. http://dx.doi.org/10.1134/s0005117918010071.

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40

Orabona, Francesco, Koby Crammer, and Nicolò Cesa-Bianchi. "A generalized online mirror descent with applications to classification and regression." Machine Learning 99, no. 3 (2014): 411–35. http://dx.doi.org/10.1007/s10994-014-5474-8.

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41

Juditsky, A. B., A. V. Nazin, A. B. Tsybakov, and N. Vayatis. "Recursive Aggregation of Estimators by the Mirror Descent Algorithm with Averaging." Problems of Information Transmission 41, no. 4 (2005): 368–84. http://dx.doi.org/10.1007/s11122-006-0005-2.

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42

Semenov, V. V. "A Version of the Mirror descent Method to Solve Variational Inequalities*." Cybernetics and Systems Analysis 53, no. 2 (2017): 234–43. http://dx.doi.org/10.1007/s10559-017-9923-9.

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43

Bubeck, Sébastien, Michael B. Cohen, James R. Lee, and Yin Tat Lee. "Metrical Task Systems on Trees via Mirror Descent and Unfair Gluing." SIAM Journal on Computing 50, no. 3 (2021): 909–23. http://dx.doi.org/10.1137/19m1237879.

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44

Nazin, A. V., S. V. Anulova, and A. A. Tremba. "A mirror descent algorithm for minimization of mean Poisson flow driven losses." Automation and Remote Control 75, no. 6 (2014): 1010–16. http://dx.doi.org/10.1134/s0005117914060022.

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45

Boţ, Radu Ioan, and Axel Böhm. "An incremental mirror descent subgradient algorithm with random sweeping and proximal step." Optimization 68, no. 1 (2018): 33–50. http://dx.doi.org/10.1080/02331934.2018.1482491.

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46

Bayadina, A., A. Gasnikov, E. Gasnikova, and S. Matsiyevsky. "Direct-dual method of mirror descent for conditional problems of stochastic optimization." Журнал вычислительной математики и математической физики 58, no. 11 (2018): 1794–803. http://dx.doi.org/10.31857/s004446690003533-7.

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47

Borovykh, A., N. Kantas, P. Parpas, and G. A. Pavliotis. "On stochastic mirror descent with interacting particles: Convergence properties and variance reduction." Physica D: Nonlinear Phenomena 418 (April 2021): 132844. http://dx.doi.org/10.1016/j.physd.2021.132844.

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48

Stonyakin, Fedor Sergeevich, Aleksej N. Stepanov, Alexander Vladimirovich Gasnikov, and Alexander A. Titov. "Mirror descent for constrained optimization problems with large subgradient values of functional constraints." Computer Research and Modeling 12, no. 2 (2020): 301–17. http://dx.doi.org/10.20537/2076-7633-2020-12-2-301-317.

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49

Majlesinasab, Nahidsadat, Farzad Yousefian, and Arash Pourhabib. "Self-Tuned Mirror Descent Schemes for Smooth and Nonsmooth High-Dimensional Stochastic Optimization." IEEE Transactions on Automatic Control 64, no. 10 (2019): 4377–84. http://dx.doi.org/10.1109/tac.2019.2897889.

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50

Gasnikov, A. V., Yu E. Nesterov, and V. G. Spokoiny. "On the efficiency of a randomized mirror descent algorithm in online optimization problems." Computational Mathematics and Mathematical Physics 55, no. 4 (2015): 580–96. http://dx.doi.org/10.1134/s0965542515040041.

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