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We propose a new method to improve the convergence speed of the Robbins-Monroalgorithm by introducing prior information about the target point into theRobbins-Monro iteration. We achieve the incorporation of prior informationwithout the need of a -- potentially wrong -- regression model, which wouldalso entail additional constraints. We show that this prior-informationRobbins-Monro sequence is convergent for a wide range of prior distributions,even wrong ones, such as Gaussian, weighted sum of Gaussians, e.g., in a kerneldensity estimate, as well as bounded arbitrary distribution functions greaterthan zero. We furthermore analyse the sequence numerically to understand itsperformance and the influence of parameters. The results demonstrate that theprior-information Robbins-Monro sequence converges faster than the standardone, especially during the first steps, which are particularly important forapplications where the number of function measurements is limited, and when thenoise of observing the underlying function is large. We finally propose a ruleto select the parameters of the sequence.

A Robbins--Monro Sequence That Can Exploit Prior Information For Faster Convergence