Parameter-Free Dynamic Regret under Heavy-Tailed Noise
We study online convex optimization with one unbiased stochastic subgradient per round and noise having a finite $p$-th central moment, where $p\in(1,2]$ is unknown. For a bounded convex domain of diameter $D$, subgradients bounded by $G$, noise scale $σ$, and comparator path length $P_T$, let $Λ_T=1+P_T/D$. A single algorithm, using none of $G,σ,p,P_T$, attains expected dynamic regret $O_p\left(\min\{GD\sqrt{TΛ_T}+σDT^{1/p}Λ_T^{(p-1)/p},\,GDT\}\right)$ against every fixed comparator sequence. Restarted AdaGrad experts produce the noise-path exponent $(p-1)/p$, and a prior favoring longer restart intervals removes horizon-dependent logarithmic overhead. We give an explicit bound uniform i...
| Authors | Vaneet Aggarwal |
|---|---|
| Primary category | cs.LG |
| Published | 29 July 2026 |
| Last updated at source | 22 September 2026 |
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