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.

本研究通过线性随机逼近（LSA）算法与马尔可夫数据研究了使用恒定步长进行统计推断的有效性。通过建立中心极限定理（CLT），我们提出了一种使用平均 LSA 迭代构建置信区间（CIs）的推断过程。我们的方法利用恒定步长 LSA 的快速混合特性进行更好的协方差估计，并采用 Richardson-Romberg（RR）外推方法来减少恒定步长和马尔可夫数据引起的偏差。我们在 RR 外推中开发了用于指导步长选择的理论结果，并确定了几个重要设置，在没有外推的情况下，偏差可以证明消失。我们进行了大量的数值实验，并与传统推断方法进行比较。我们的结果表明，使用恒定步长在超参数调整、快速收敛和一致性更好的置信区间覆盖方面具有优势，尤其是在数据有限的情况下。