Central Limit Theorems for Stochastic Approximation with controlled Markov chain dynamics
By Gersende Fort. 2013
54 citations recorded by the source corpus.
This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated average sequence is also established. The originality of this paper is to address the case of controlled Markov chain dynamics $\{X_n, n\geq 0 \}$ and the case of multiple targets. The framework also accomodates (randomly) truncated SA algorithms. Sufficient conditions for CLT's to hold are provided as well as comments on how these conditions extend previous works (such as independent and identically distributed dynamics, the Robbins-Monro dynamic or the single target case). The paper gives a special emphasis on how these conditions hold for SA with controlled Markov chain dynamics and multiple targets; it is proved that this paper improves on existing works.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/25b186c2e5d13a2dad0766287fde98d7c2e75084
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Citations in the corpus
- Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity (2017, result): “Such results are generally achieved asymptotically in general situations where f is assumed to be strongly convex, we refer to [PJ92] for the initial asymptotic description and to [For15] for some more general results.”