Effectiveness of Constant Stepsize in Markovian LSA and Statistical
  Inference
Dongyan Huo Yudong Chen Qiaomin Xie
In this paper, we study the effectiveness of using a constant stepsize in
statistical inference via linear stochastic approximation (LSA) algorithms with
Markovian data. After establishing a Central Limit Theorem (CLT), we outline an
inference procedure that uses averaged LSA iterates to construct confidence
intervals (CIs). Our procedure leverages the fast mixing property of
constant-stepsize LSA for better covariance estimation and employs
Richardson-Romberg (RR) extrapolation to reduce the bias induced by constant
stepsize and Markovian data. We develop theoretical results for guiding
stepsize selection in RR extrapolation, and identify several important settings
where the bias provably vanishes even without extrapolation. We conduct
extensive numerical experiments and compare against classical inference
approaches. Our results show that using a constant stepsize enjoys easy
hyperparameter tuning, fast convergence, and consistently better CI coverage,
especially when data is limited.