Stochastic approximation with state-dependent noise

摘要

The purpose of stochastic approximation (SA) is to find the rootsof f(.) or the maximiz- er (minimizer) of L(.) when the unknownfunction f(.) or L(.) can be observed but with noise. Sa is animportant tool in dealing with many problems arising from systems andcontrol, whose solutions oftn rely on convergence of the SA algorithmapplied. Here the pathwise convergance of SA algo- rithms isconsidered, when the observation noise may depend on state by whichwe mean those x at which F(x) or L(x) are observed.