RanSOM uses randomized scaling in second-order momentum updates to obtain unbiased bias estimates via Stein identities, recovering optimal O(ε^{-3}) rates for bounded and heavy-tailed noise in constrained and unconstrained settings.
Substituting η= min(η i) into the drift term yields the sum of the inverse rates: Cinit gap Tmin(η i) ≤ X i Cinit gap T ηi
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RanSOM: Second-Order Momentum with Randomized Scaling for Constrained and Unconstrained Optimization
RanSOM uses randomized scaling in second-order momentum updates to obtain unbiased bias estimates via Stein identities, recovering optimal O(ε^{-3}) rates for bounded and heavy-tailed noise in constrained and unconstrained settings.