הערכה סטוכסטית קבוע-צעד: סופר-טיפול, הערכה גאוסיאנית וגבולות זנב

תקציר מקורי באנגליתarXiv:2602.13960v2 Announce Type: replace Abstract: Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency, yet the distribution of the iterates is typically intractable. Classical asymptotics results give $X_k^{(\alpha)} \approx X^{(\alpha)} \approx x^\star+\sqrt{\alpha}Y$, where $X^{(\alpha)}$ is the steady state and $Y$ is an appropriate Gaussian limit, by progressively taking the time $k\uparrow\infty$ and stepsize $\alpha\downarrow0$. Such limit results, however, do not quantify finite-time, finite-stepsize errors. We develop an explicit pre-limit characterization for SA with i.i.d.\ and Markovian noise. We establish existence and uniqueness of the stationary law, a geometric Wasserstein convergence to stationarity, and almost-sure and