Non-Asymptotic Convergence of Stochastic Iterative Algorithms: A Lyapunov Framework

ArXi:2605.31309v1 Announce Type: new We survey Lyapuno-based techniques for the finite-time analysis of stochastic iterative algorithms, also known as stochastic approximation (SA) algorithms, for solving fixed-point equations $\bar{F}(x)=x$, where the operator $\bar{F}(\cdot)$ can only be accessed through a noisy oracle. We first focus on the standard setting in which $\bar{F}(\cdot)$ is contractive with respect to some norm and the noise is i.i.d., and explain how generalized Moreau envelopes serve as universal Lyapuno functions, regardless of the underlying norm.