Fetching the paper…
Reading the bibliography…
This paper studies the asymptotic behavior of the constant step Stochastic Gradient Descent for the minimization of an unknown function F , defined as the expectation of a non convex, non smooth, locally Lipschitz random function.
The averaging principle for parabolic and elliptic differential equations and Markov processes with small diffusion
R. Z. Has’minskiĭ · 1963
Earlier work this paper cites.
Generic differentiability of Lipschitzian functions
G. Lebourg · 1979
Earlier work this paper cites.
Generalized-differentiable functions
V.I. Norkin · 1980
Earlier work this paper cites.
Differential inclusions
J.-P. Aubin and A. Cellina · 1984
Earlier work this paper cites.
Methods of nonconvex optimization
VS Mikhalevich, AM Gupal, and VI Norkin · 1987
Earlier work this paper cites.
Adaptive algorithms and stochastic approximations
A. Benveniste, M. Métivier, and P. Priouret · 1990
Earlier work this paper cites.
Poincaré’s recurrence theorem for set-valued dynamical systems
J.-P. Aubin, H. Frankowska, and A. Lasota · 1991
Earlier work this paper cites.
Geometric categories and o-minimal structures
L. van den Dries and C. Miller · 1996
Earlier work this paper cites.
Nonsmooth analysis and control theory
F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski · 1998
Earlier work this paper cites.
Stochastic generalized gradient method for solving nonconvex nonsmooth stochastic optimization problems
Y.M. Ermoliev and V.I. Norkin · 1998
Cited alongside, same era.
Solution of nonconvex nonsmooth stochastic optimization problems
Y. M. Ermoliev and VI Norkin · 2003
Cited alongside, same era.
Stochastic approximation and recursive algorithms and applications
H. J. Kushner and G. G. Yin · 2003
Cited alongside, same era.
Stochastic approximations and differential inclusions
M. Benaïm, J. Hofbauer, and S. Sorin · 2005
Cited alongside, same era.
Infinite Dimensional Analysis: a Hitchhiker’s Guide
C. D. Aliprantis and K. C. Border · 2006
Cited alongside, same era.
Clarke subgradients of stratifiable functions
J. Bolte, A. Daniilidis, A. Lewis, and M. Shiota · 2007
Cited alongside, same era.
Real Analysis: Modern Techniques and Their Applications
G.B. Folland · 2013
Later among the works it cites.
Stochastic approximations with constant step size and differential inclusions
G. Roth and W. H. Sandholm · 2013
Later among the works it cites.
Automatic differentiation in PyTorch
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer · 2017
Later among the works it cites.
Provably correct automatic sub-differentiation for qualified programs
S. Kakade and J. D. Lee · 2018
Later among the works it cites.
Analysis of nonsmooth stochastic approximation: the differential inclusion approach
S. Majewski, B. Miasojedow, and E. Moulines · 2018
Later among the works it cites.
Constant step stochastic approximations involving differential inclusions: stability, long-run convergence and applications
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
An invitation to tame optimization
A. D. Ioffe · 2009
Cited alongside, same era.
Markov Chains and Stochastic Stability
S. Meyn and R. L. Tweedie · 2009
Cited alongside, same era.
Ergodic properties of weak asymptotic pseudotrajectories for set-valued dynamical systems
M. Faure and G. Roth · 2013
Cited alongside, same era.
P. Bianchi, W. Hachem, and A. Salim · 2019
Later among the works it cites.
J. Bolte and E. Pauwels · 2019
Later among the works it cites.
Stochastic subgradient method converges on tame functions
D. Davis, D. Drusvyatskiy, S. Kakade, and J. D. Lee · 2020
Closest in time.
Convergence of a stochastic subgradient method with averaging for nonsmooth nonconvex constrained optimization
Andrzej Ruszczyński · 2020
Closest in time.