Markovian stochastic approximation with expanding projections

Details Markovian stochastic approximation with expanding projections Markovian stochastic approximation with expanding projections

2011-11-23

arxiv.org/abs/1111.5421v1

Mathematics

Probability

36 pages, 1 figure

Scientific paper

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\'ottir [Oper. Res. 43 (2010) 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.

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