AI RESEARCH
Online Convex Optimization with Heavy Tails: Old Algorithms, New Regrets, and Applications
arXiv CS.LG
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ArXi:2508.07473v3 Announce Type: replace In Online Convex Optimization (OCO), when the stochastic gradient has a finite variance, many algorithms provably work and guarantee a sublinear regret. However, limited results are known if the gradient estimate has a heavy tail, i.e., the stochastic gradient only admits a finite $\mathsf{p}$-th central moment for some $\mathsf{p}\in\left(1,2\right]$. Motivated by it, this work examines different old algorithms for OCO (e.g., Online Gradient Descent) in the challenging heavy-tailed setting.