A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci, vol.2, issue.1, pp.183-202, 2009. ,
Adaptivity of averaged stochastic gradient descent to local strong convexity for logistic regression, Journal of Machine Learning Research, vol.15, pp.595-627, 2014. ,
Les algorithmes stochastiques contournent-ils lespì eges ? Annales de l'I.H.P. Probabilités et Statistiques, pp.395-427, 1996. ,
Dynamics of stochastic approximation algorithms, Séminaire de Probabilités XXXIII, 2006. ,
Asymptotic pseudotrajectories and chain recurrent flows, with applications, Journal of Dynamics and Differential Equations, vol.24, issue.1, pp.141-176, 1996. ,
DOI : 10.1007/BF02218617
Convergence of Probability Measures Wiley series in Probability & Statistics, 1995. ,
Concentration inequalities A nonasymptotic theory of independence ,
URL : https://hal.archives-ouvertes.fr/hal-00794821
Self-interacting diffusions. Probab. Theory Related Fields, pp.1-41, 2002. ,
Non-asymptotic analysis of stochastic approximation algorithms for machine learning, Advances in Neural Information Processing Systems (NIPS), 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00608041
Convex optimization, 2004. ,
On the long time behavior of second order differential equations with asymptotically small dissipation, Trans. Amer. Math. Soc, issue.11, pp.3615983-6017, 2009. ,
Second-order differential equations with asymptotically small dissipation and piecewise flat potentials, Proceedings of the Seventh Mississippi State?UAB Conference on Differential Equations and Computational Simulations, pp.33-38, 2009. ,
Random iterative models, adaptive algorithms and stochastic approximations, Applications of Mathematics, vol.22, 1997. ,
From averaging to acceleration, there is only a step-size, Proceedings of the International Conference on Learning Theory (COLT), 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01136945
An algorithm for quadratic programming, Naval Research Logistics Quarterly, vol.3, issue.1-2, pp.95-110, 1956. ,
DOI : 10.1002/nav.3800030109
Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming, SIAM Journal on Optimization, vol.23, issue.4, pp.2341-2368, 2013. ,
DOI : 10.1137/120880811
URL : http://arxiv.org/abs/1309.5549
Accelerated gradient methods for nonconvex nonlinear and stochastic programming, Mathematical Programming, vol.19, issue.1, pp.59-99, 2016. ,
DOI : 10.1007/s10107-015-0871-8
URL : http://arxiv.org/abs/1310.3787
A stochastic model for speculative bubbles. Alea: Latin American journal of probability and mathematical statistics, pp.491-532, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00937447
Long time behaviour and stationary regime of memory gradient diffusions, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.50, issue.2, pp.564-601, 2014. ,
DOI : 10.1214/12-AIHP536
URL : https://hal.archives-ouvertes.fr/hal-00757068
Ordinary Differential Equations, Classic in Applied Mathematics, 1982. ,
Accelerated gradient methods for stochastic optimization and online learning, Advances in Neural Information Processing Systems, 2009. ,
Stochastic Estimation of the Maximum of a Regression Function, The Annals of Mathematical Statistics, vol.23, issue.3, pp.462-466, 1952. ,
DOI : 10.1214/aoms/1177729392
Stochastic approximation and recursive algorithms and applications, 2003. ,
An optimal method for stochastic composite optimization, Mathematical Programming, vol.24, issue.1-2, pp.365-397, 2012. ,
DOI : 10.1007/s10107-010-0434-y
An adaptive scheme for the approximation of dissipative systems, Stochastic Processes and their Applications, pp.1491-1518, 2007. ,
Gradient descent converges to minimizers, 2016. ,
Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Processes and their Applications, vol.101, issue.2, pp.185-232, 2002. ,
DOI : 10.1016/S0304-4149(02)00150-3
URL : http://doi.org/10.1016/s0304-4149(02)00150-3
Stability of Markovian processes. III. Foster-Lyapunov criteria for continuous-time processes, Adv. in Appl. Probab, vol.25, issue.3, pp.518-548, 1993. ,
Problem complexity and method efficiency in optimization, Wiley-Interscience Series in Discrete Mathematics, 1983. ,
Non-convergence to unstable points in urn models and stochastic approximations, Annals of Probability, vol.18, pp.698-712, 1990. ,
Acceleration of Stochastic Approximation by Averaging, SIAM Journal on Control and Optimization, vol.30, issue.4, pp.838-855, 1992. ,
DOI : 10.1137/0330046
Mémoire sur les courbes définies par uné equation différentielle (iv), Journal de Mathématiques Pures et Appliquées, vol.4, pp.151-217, 1886. ,
Some methods of speeding up the convergence of iteration methods, USSR Computational Mathematics and Mathematical Physics, vol.4, pp.1-17, 1964. ,
A Stochastic Approximation Method, The Annals of Mathematical Statistics, vol.22, issue.3, pp.400-407, 1951. ,
DOI : 10.1214/aoms/1177729586
Efficient estimations from a slowly convergent robbins-monro process, 1988. ,
Probability for Analysts, 1994. ,
Multidimensional diffusion processes, Classics in Mathematics, 2006. ,
DOI : 10.1007/3-540-28999-2
A differential equation for modeling nesterov's accelerated gradient method: theory and insights, Journal of Machine Learning Research, 2016. ,
Unified convergence analysis of stochastic momentum methods for convex and non-convex optimization, 2016. ,