Oracle Complexity of Stochastic Fixed-Point Equations with Nonexpansive Maps
We study the oracle complexity of computing a point with small fixed-point residual $\|T(x)-x\| \leq ε$, for a general norm $\|\cdot\|$ and a self-map $T$ of a compact convex set. We study this problem in the setting where $T$ is nonexpansive with respect to the same norm $\|\cdot\|$ and accessed via an unbiased stochastic oracle with bounded variance $σ^2$. We provide an algorithm that solves such instances for any norm with a weak Rademacher type $q > 1$, with high probability. The algorithm is based on a recursive anchoring technique. For type-$2$ spaces, such as $\ell_p$-spaces for $p \in [2, \infty]$, our algorithm attains stochastic oracle complexity $\tilde O(σ^2 ε^{-3} + ε^{-1})$....
| Authors | Jelena Diakonikolas, Cristóbal Guzmán, David Martínez-Rubio |
|---|---|
| Primary category | math.OC |
| Published | 8 September 2026 |
| Last updated at source | 8 September 2026 |
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