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We present a stochastic trust-region model-based framework in which itsradius is related to the probabilistic models. Especially, we propose aspecific algorithm, termed STRME, in which the trust-region radius dependslinearly on the latest model gradient. The complexity of STRME method innon-convex, convex and strongly convex settings has all been analyzed, whichmatches the existing algorithms based on probabilistic properties. In addition,several numerical experiments are carried out to reveal the benefits of theproposed methods compared to the existing stochastic trust-region methods andother relevant stochastic gradient methods.

Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models