2011/11/30 by Christophe Andrieu, Matti Vihola · 17 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Convergence (economics) #Convergence of random variables #Focus (optics) #Markov Chains and Monte Carlo Methods #Markov chain #Markov process #Range (aeronautics) #Stability (learning theory) #Stochastic Gradient Optimization Techniques #Stochastic approximation #Stochastic process #Stochastic processes and financial applications #math.PR #stat.CO #stat.ME
paper · pdf · doi:10.3150/12-bej497
published in Bernoulli 20(2) (Chapman and Hall London) · 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)
openalex publication_date 2014/02/28 · arxiv created 2014/03/07 · arxiv updated 2014/03/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 Andradóttir [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.