A stopped stochastic approximation algorithm
A stopping time problem for a multidimensional Robbins-Monro stochastic approximation procedure is studied. The stopping rule is determined such that the procedure will be terminated if the unknown parameter \(\theta\) (the root of the regression function) is inside a desired ellipsoidal confidence region with high probability. Some usual assumptions are supposed to be valid for this stochastic approximation procedure. The noise processes are supposed to fulfill a condition of martingale type but not to be necessarily independent. The stopped process is then shown to be asymptotically normal by means of weak convergence methods. The construction of the desired confidence ellipsoids is described.
multidimensional Robbins-Monro stochastic approximation procedure
scientific article; zbMATH DE number 4064312
scientific article