Before revision:  It has been observed empirically that AA may speed up asymptotic ADMM convergence by a large amount for various applications in data science and machine learning, but there are no known convergence bounds for AA with finite window size that would allow quantification of this improvement in asymptotic convergence speed. We discuss an approach to quantify the improved linear asymptotic convergence factor that is based on computing the optimalasymptotic convergence factor for a stationary version of AA applied to ADMM . Numerical tests show that this allows us to estimate the asymptotic linear convergence factor of AA with finite window size applied to ADMM.
After revision:  We do so by considering the spectral properties of the Jacobians of ADMM and a stationary version of AA evaluated at the fixed point, where the coefficients of the stationary version are computed such that its asymptotic linear convergence factor is optimal . Numerical tests show that this allows us to estimate the asymptotic linear convergence factor of AA with finite window size applied to ADMM.