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A convergence analysis of the perturbed compositional gradient flow: Averaging principle and normal deviations
Discrete and Continuous Dynamical Systems. Series A
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion is given by an averaged ordinary differential equation. We then demonstrate that the deviation of the slow motion from the averaged equation, after proper rescaling, converges to a stochastic process with Gaussian inputs. This indicates that the slow motiondoi:10.3934/dcds.2018216 fatcat:mmfooim5fngjbcmrxytnr26i4e