Markovian stochastic approximation with expanding projections

Journal article

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. © 2014 ISI/BS.

Authors: Andrieu, C; Vihola, M

• Publisher: International Statistical Institute
• Journal: Bernoulli
• Volume: 20
• Issue: 2
• Pages: 545-585
• Publication date: 2014-01-01
• DOI: 10.3150/12-BEJ497
• ISSN: 1350-7265
• Language: English
• Keywords: Stochastic approximation; Particle Markov chain Monte Carlo; Independent Metropolis-Hastings; Stability; Expectation maximisation