Prediction with Expert Advice under Heavy-Tailed Losses
We study prediction with expert advice over $T$ rounds with $K$ experts under heavy-tailed losses whose $(1+ε)$-moment is bounded by $θ>0$ for some $ε\in(0,1]$. In this setting, existing algorithms designed for the case $ε=1$ can be suboptimal when $ε<1$, suffering an additional polynomial dependence on $K$. We characterize the minimax pseudo-regret rate as $Θ((θT)^{\frac{1}{1+ε}}(\log K)^{\fracε{1+ε}})$ and establish gap-dependent lower bounds in a self-bounded environment. To attain this minimax rate without prior knowledge of either $ε$ or $θ$, we propose Adaptive Heavy-Tailed FTRL, which uses robust data-dependent scale adaptation together with truncation. We further develop Adaptive ...
| Authors | Yuki Shibukawa, Shinji Ito |
|---|---|
| Primary category | cs.LG |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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