A moderate deviation principle holds for the stochastic approximation recursion X_{n+1} = X_n + (b/(n+1))[g(X_n) + U_{n+1}] with bounded martingale differences U_n.
Renlund, Limit theorem for stochastic approximation algorithm
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Moderate Deviation Principle for a Stochastic Approximation Process
A moderate deviation principle holds for the stochastic approximation recursion X_{n+1} = X_n + (b/(n+1))[g(X_n) + U_{n+1}] with bounded martingale differences U_n.