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In this paper we study the limit of the value function for a two-scale,infinite-dimensional, stochastic controlled system with cylindrical noise andpossibly degenerate diffusion. The limit is represented as the value functionof a new reduced control problem (on a reduced state space). The presence of acylindrical noise prevents representation of the limit by viscosity solutionsof HJB equations, while degeneracy of diffusion coefficients preventsrepresentation as a classical BSDE. We use a vanishing noise regularizationtechnique.

Singular Limit of Two Scale Stochastic Optimal Control Problems in Infinite Dimensions by Vanishing Noise Regularization