English

Markovian stochastic approximation with expanding projections

Probability 2014-03-10 v2 Computation Methodology

Abstract

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We study a stochastic approximation procedure with expanding projections similar to Andrad\'{o}ttir [Oper. Res. 43 (1995) 1037-1048]. We focus on Markovian noise and show the stability and convergence under general conditions. Our framework also incorporates the possibility to use a random step size sequence, which allows us to consider settings with a non-smooth family of Markov kernels. We apply the theory to stochastic approximation expectation maximisation with particle independent Metropolis-Hastings sampling.

Keywords

Cite

@article{arxiv.1111.5421,
  title  = {Markovian stochastic approximation with expanding projections},
  author = {Christophe Andrieu and Matti Vihola},
  journal= {arXiv preprint arXiv:1111.5421},
  year   = {2014}
}

Comments

Published in at http://dx.doi.org/10.3150/12-BEJ497 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

R2 v1 2026-06-21T19:40:19.364Z