Fetching the paper…
Reading the bibliography…
In this paper we study the asymptotic behavior of stochastic approximation schemes with set-valued drift function and non-additive iterate-dependent Markov noise.
M. Metivier and P. Priouret, “Applications of a Kushner and Clark lemma to general classes of stochastic algorithms,” IEEE Transactions on Information Theory , vol. 30, no. 2, pp. 140–151, 1984
1984
Earlier work this paper cites.
V. S. Borkar, “Optimal control of diffusion processes,” in Pitman Research Notes in Math., 203. 36 Borkar V.(2005):“Controlled diffusion processes”, Probability surveys . Citeseer, 1989
1989
Earlier work this paper cites.
M. Benaim, “A dynamical system approach to stochastic approximations,” SIAM Journal on Control and Optimization , vol. 34, no. 2, pp. 437–472, 1996
1996
Earlier work this paper cites.
V. Tadić, “Stochastic approximation with random truncations, state-dependent noise and discontinuous dynamics,” Stochastics: An International Journal of Probability and Stochastic Processes , vol. 64, no. 3-4, pp. 283–326, 1998
1998
Earlier work this paper cites.
M. Benaïm, “Dynamics of stochastic approximation algorithms,” in Seminaire de probabilites XXXIII . Springer, 1999, pp. 1–68
1999
Earlier work this paper cites.
V. S. Borkar and S. P. Meyn, “The ODE method for convergence of stochastic approximation and reinforcement learning,” SIAM Journal on Control and Optimization , vol. 38, no. 2, pp. 447–469, 2000
2000
Earlier work this paper cites.
M. Benaïm, J. Hofbauer, and S. Sorin, “Stochastic approximations and differential inclusions,” SIAM Journal on Control and Optimization , vol. 44, no. 1, pp. 328–348, 2005
2005
Earlier work this paper cites.
V. S. Borkar, “Stochastic approximation with ‘controlled Markov’ noise,” Systems & control letters , vol. 55, no. 2, pp. 139–145, 2006
2006
Cited alongside, same era.
V. S. Borkar, Stochastic approximation : a dynamical systems viewpoint . Cambridge University Press, 2008
2008
Cited alongside, same era.
J.-P. Aubin, Viability theory . Springer Science & Business Media, 2009
2009
Cited alongside, same era.
D. P. Bertsekas, Convex optimization theory . Athena Scientific Belmont, 2009
2009
Cited alongside, same era.
——, Probability theory: an advanced course . Springer Science & Business Media, 2012
2012
Cited alongside, same era.
S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability . Springer Science & Business Media, 2012
S. Perkins, D. S. Leslie et al. , “Asynchronous stochastic approximation with differential inclusions,” Stochastic Systems , vol. 2, no. 2, pp. 409–446, 2012
2012
Later among the works it cites.
A. Nagurney and D. Zhang, Projected dynamical systems and variational inequalities with applications . Springer Science & Business Media, 2012, vol. 2
2012
Later among the works it cites.
S. Li, Y. Ogura, and V. Kreinovich, Limit theorems and applications of set-valued and fuzzy set-valued random variables . Springer Science & Business Media, 2013, vol. 43
2013
Later among the works it cites.
C. Andrieu, M. Vihola et al. , “Markovian stochastic approximation with expanding projections,” Bernoulli , vol. 20, no. 2, pp. 545–585, 2014
2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2012
Cited alongside, same era.
J.-P. Aubin and A. Cellina, Differential inclusions: set-valued maps and viability theory . Springer Science & Business Media, 2012, vol. 264
2012
Cited alongside, same era.
2015
Later among the works it cites.
G. Fort, E. Moulines, A. Schreck, and M. Vihola, “Convergence of Markovian stochastic approximation with discontinuous dynamics,” SIAM Journal on Control and Optimization , vol. 54, no. 2, pp. 866–893, 2016
2016
Closest in time.