新闻 · arXiv cs.LG

Solving Stochastic Fixed-Point Equations with High Probability

We study stochastic fixed-point equations $\mathbf{T}(\mathbf{x}) = \mathbf{x}$ over normed spaces $(\mathcal{E}, \|\cdot\|)$, where the operator $\mathbf{T}$ is nonexpansive or contractive and is accessed only through unbiased stochastic evaluations with bounded second central moment. Given $ε> 0, δ\in (0, 1)$, the goal is to output $\mathbf{x} \in \mathcal{E}$ such that $\|\mathbf{T}(\mathbf{x}) - \mathbf{x}\| \leq ε$ with probability at least $1-δ$. We introduce VR-GHAL, a variance-reduced…