Geodesic
On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere
Matematičeskie zametki, Tome 106 (2019) no. 1, pp. 13-23.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of constructing upper bounds for the expectation of the norm of a vector uniformly distributed on the Euclidean unit sphere.
Keywords: concentration of measure, vector uniformly distributed on the sphere. 
@article{MZM_2019_106_1_a1,
     author = {E. A. Gorbunov and E. Vorontsova and A. V. Gasnikov},
     title = {On the {Upper} {Bound} for the {Expectation} of the {Norm} of a {Vector} {Uniformly} {Distributed} on the {Sphere} and the {Phenomenon} of {Concentration} of {Uniform} {Measure} on the {Sphere}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {13--23},
     publisher = {mathdoc},
     volume = {106},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a1/}
}
TY  - JOUR
AU  - E. A. Gorbunov
AU  - E. Vorontsova
AU  - A. V. Gasnikov
TI  - On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere
JO  - Matematičeskie zametki
PY  - 2019
SP  - 13
EP  - 23
VL  - 106
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a1/
LA  - ru
ID  - MZM_2019_106_1_a1
ER  - 
%0 Journal Article
%A E. A. Gorbunov
%A E. Vorontsova
%A A. V. Gasnikov
%T On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere
%J Matematičeskie zametki
%D 2019
%P 13-23
%V 106
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a1/
%G ru
%F MZM_2019_106_1_a1
E. A. Gorbunov; E. Vorontsova; A. V. Gasnikov. On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere. Matematičeskie zametki, Tome 106 (2019) no. 1, pp. 13-23. http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a1/

[1] E. Vorontsova, A. Gasnikov, E. Gorbunov, Accelerated Directional Search with Non-Euclidean Prox-Structure, 2019, arXiv: 1710.00162

[2] A. Gasnikov, A. Lagunovskaya, I. Usmanova, F. Fedorenko, Gradient-Free Prox-Methods with Inexact Oracle for Stochastic Convex Optimization Problems on a Simplex, 2014, arXiv: 1412.3890

[3] A. V. Gasnikov, A. A. Lagunovskaya, I. N. Usmanova, F. A. Fedorenko, “Bezgradientnye prokc-metody s netochnym orakulom dlya negladkikh zadach vypukloi stokhasticheskoi optimizatsii na simplekse”, Avtomat. i telemekh., 2016, no. 10, 57–77 | Zbl

[4] O. Shamir, An Optimal Algorithm for Bandit and Zero-Order Convex Optimization with Two-Point Feedback, 2015, arXiv: 1507.08752

[5] O. Shamir, “An optimal algorithm for bandit and zero-order convex optimization with two-point feedback”, J. Mach. Learn. Res., 18 (2017), Paper No. 52 | MR | Zbl

[6] J. C. Duchi, M. I. Jordan, M. J. Wainwright, A. Wibisono, “Optimal rates for zero-order convex optimization: the power of two function evaluations”, IEEE Trans. Inform. Theory, 61:5 (2015), 2788–2806 | DOI | MR | Zbl

[7] A. Blum, J. Hopcroft, R. Kannan, Foundations of Data Science, , 2018 https://www.cs.cornell.edu/jeh/book.pdf

[8] K. Ball, “An elementary introduction to modern convex geometry”, Flavors of Geometry, Math. Sci. Res. Inst. Publ., 31, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[9] L. Bogolubsky, P. Dvurechensky, A. Gasnikov, G. Gusev, Yu. Nesterov, A. Raigorodskii, A. Tikhonov, M. Zhukovskii, Learning Supervised PageRank with Gradient-Based and Gradient-Free Optimization Methods, , 2016 https://papers.nips.cc/paper/6565-learning-supervised-pagerank-with-gradient-based-and-gradient-free-optimization-methods.pdf

[10] S. Boucheron, G. Lugosi, P. Massart, Concentration Inequalities. A Nonasymptotic Theory of Independence, Oxford Univ. Press, Oxford, 2013 | MR | Zbl

[11] V. Milman, G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Lecture Notes in Math., 1200, Springer-Verlag, Berlin, 1986 | DOI | MR | Zbl

[12] V. A. Zorich, Matematicheskii analiz v zadachakh estestvoznaniya, MTsNMO, M., 2008

[13] A. Bayandina, A. Gasnikov, F. Guliev, A. Lagunovskaya, Gradient-Free Two-Points Optimal Method for Non Smooth Stochastic Convex Optimization Problem with Additional Small Noise, , 2017 1701.03821

[14] M. Lifshits, Lectures on Gaussian Processes, Springer, Heidelberg, 2012 | MR | Zbl

[15] E. A. Gorbunov, E. A. Vorontsova, Vychislitelnye eksperimenty, illyustriruyuschie yavlenie kontsentratsii ravnomernoi mery na poverkhnosti evklidovoi sfery v maloi okrestnosti ekvatora, , 2015 https://github.com/evorontsova/Concentration-of-Measure