A single-loop Riemannian stochastic smoothing method with recursive momentum attains O(epsilon^-3) iteration complexity for Lipschitz nonsmooth terms, and O~(epsilon^{-max{theta+2,2theta}}) under an error-bound condition for constraints.
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Single-loop $\mathcal{O}(\epsilon^{-3})$ stochastic smoothing algorithms for nonsmooth Riemannian optimization
A single-loop Riemannian stochastic smoothing method with recursive momentum attains O(epsilon^-3) iteration complexity for Lipschitz nonsmooth terms, and O~(epsilon^{-max{theta+2,2theta}}) under an error-bound condition for constraints.