Adaptive stepsize selection for tracking in a regime-switching environment

Authors:
Andre Costa;Felisa J. Vázquez-Abad
Affiliations:
ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, University of Melbourne, 3010, Australia;Department of Mathematics and Statistics, University of Melbourne, 3010, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

We consider the problem of using a stochastic approximation algorithm to perform online tracking in a non-stationary environment characterised by abrupt ''regime changes''. The primary contribution of this paper is a new approach for adaptive stepsize selection that is suitable for this type of non-stationarity. Our approach is pre-emptive rather than reactive, and is based on a strategy of maximising the rate of adaptation, subject to a constraint on the probability that the iterates fall outside a pre-determined range of acceptable error. The basis for our approach is provided by the theory of weak convergence for stochastic approximation algorithms.