A. Agarwal, P. L. Bartlett, P. Ravikumar, and M. J. Wainwright, Information-Theoretic Lower Bounds on the Oracle Complexity of Stochastic Convex Optimization, IEEE Transactions on Information Theory, vol.58, issue.5, pp.3235-3249595, 2012.
DOI : 10.1109/TIT.2011.2182178

J. Bolte, A. Daniilidis, O. Ley, and L. Mazet, Characterizations of ??ojasiewicz inequalities: Subgradient flows, talweg, convexity, Transactions of the American Mathematical Society, vol.362, issue.06, pp.3319-3363, 2010.
DOI : 10.1090/S0002-9947-09-05048-X

D. P. Bertsekas, Nonlinear programming. Athena Scientific Optimization and Computation Series, Athena Scientific, 1999.

F. Bach and E. Moulines, Non-asymptotic analysis of stochastic approximation algorithms for machine learning, Advances in Neural Information Processing Systems, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00608041

J. Bolte, P. Nguyen, J. Peypouquet, and B. W. Suter, From error bounds to the complexity of first-order descent methods for convex functions, Mathematical Programming, vol.14, issue.2, pp.1-37, 2016.
DOI : 10.1137/S1052623402403505

G. Casella and R. L. Berger, Statistical Inference., Biometrics, vol.49, issue.1, 2001.
DOI : 10.2307/2532634

H. Cardot, P. Cénac, and A. Godichon-baggioni, Online estimation of the geometric median in Hilbert spaces: Nonasymptotic confidence balls, The Annals of Statistics, vol.45, issue.2, pp.591-614, 2017.
DOI : 10.1214/16-AOS1460SUPP
URL : https://hal.archives-ouvertes.fr/hal-01555593

H. Cardot, P. Cenac, and P. A. Zitt, Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm, Bernoulli, vol.19, issue.1, pp.18-43, 2013.
DOI : 10.3150/11-BEJ390
URL : https://hal.archives-ouvertes.fr/hal-00558481

A. Cabot, H. Engler, and S. Gadat, On the long time behavior of second order differential equations with asymptotically small dissipation, Transactions of the American Mathematical Society, vol.361, issue.11, pp.5983-6017, 2009.
DOI : 10.1090/S0002-9947-09-04785-0
URL : https://hal.archives-ouvertes.fr/hal-00627023

M. Duflo, Random Iterative Models, Classics in Mathematics, vol.34, 1997.
DOI : 10.1007/978-3-662-12880-0

G. Fort, Central limit theorems for stochastic approximation with controlled Markov chain dynamics, ESAIM: Probability and Statistics, vol.19, pp.60-80, 2015.
DOI : 10.1006/jmva.1996.0024
URL : https://hal.archives-ouvertes.fr/hal-00861097

S. Gadat and L. Miclo, Spectral decompositions and l2-operator norms of toy hypocoercive semi-groups. Kinetic and Related Models, pp.317-372, 2013.

J. H. Kemperman, The median of a finite measure on a banach space. Statistical data analysis based on the L 1 -norm and related methods, pp.217-230, 1987.

K. Kurdyka, On gradients of functions definable in o-minimal structures, Annales de l???institut Fourier, vol.48, issue.3, pp.769-783, 1963.
DOI : 10.5802/aif.1638

A. Nemirovski and D. Yudin, Problem complexity and method efficiency in optimization, Wiley-Interscience Series in Discrete Mathematics, 1983.

B. T. Polyak and A. Juditsky, Acceleration of Stochastic Approximation by Averaging, SIAM Journal on Control and Optimization, vol.30, issue.4, pp.838-855, 1992.
DOI : 10.1137/0330046

H. Robbins and S. Monro, A Stochastic Approximation Method, The Annals of Mathematical Statistics, vol.22, issue.3, pp.400-407, 1951.
DOI : 10.1214/aoms/1177729586

D. Ruppert, Efficient estimations from a slowly convergent robbins-monro process, 1988.