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Bregman meets L\'evy: Stochastic mirror descent with heavy-tailed noise in continuous and discrete time
arXiv:2606.03769v1 Announce Type: cross Abstract: We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input. To address this question in a principled manner, we begin by introducing a continuous-time model of SMD as a stochastic differential equation (SDE) driven by a centered L\'evy noise process with finite $p$-th order moments, $1 < p \leq...