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.
Consider the generic structure S= PT−1 t=0 CPt+1 j=1(1−β) t+1−jE[∥∇f(x j)∥∗]
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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.