For linear stochastic approximation under Markovian noise, Richardson-Romberg extrapolation cancels the linear bias and achieves the asymptotically optimal covariance.
In this paper, we consider the simplified setting of linear SA (LSA) algorithms, which estimate a solution of the linear system ¯Aθ⋆ = ¯b
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High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation
For linear stochastic approximation under Markovian noise, Richardson-Romberg extrapolation cancels the linear bias and achieves the asymptotically optimal covariance.