A quantitative theorem supplies uniform rates of convergence for stochastic quasi-Fejér monotone sequences in metric spaces by extending a deterministic regularity notion to the stochastic setting and applying it to proximal-point, Krasnoselskii-Mann, and Busemann subgradient methods.
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A translation via outer measures yields new metatheorems that extract computable bounds from non-effective proofs of probabilistic existence statements while preserving validity over finitely additive spaces.
The stochastic proximal point method converges weakly almost surely to a minimizer in Hadamard spaces under a mild growth condition on the convex integral function.
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A quantitative theorem supplies uniform rates of convergence for stochastic quasi-Fejér monotone sequences in metric spaces by extending a deterministic regularity notion to the stochastic setting and applying it to proximal-point, Krasnoselskii-Mann, and Busemann subgradient methods.
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