An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation

ArXi:2504.12922v3 Announce Type: replace-cross We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much higher level of abstraction and generality than is typically seen in the stochastic approximation literature, formulated in particular in terms of a general modulus $\tau$ that, on an intuitive level, captures an effective variant of the uniqueness in expectation of associated solutions.