Dirichlet Follow-the-Leader Closes the Gap in Simultaneous Multiclass U-Calibration
Can one forecaster attain the optimal regret rate for every bounded proper loss and also adapt to every smooth proper loss? Recent work answered this up to a dimension gap. Its self-concordant perturbation gives roughly $K^{5/4}\sqrt{T}$ worst-case regret and incurs an additional $β\sqrt{K}\log K$ for $β$-smooth losses. We close both gaps with a one-line forecaster. After observing class counts $c_{t-1}$, draw the next prediction from $\operatorname{Dir}(c_{t-1})$, on the face of classes seen so far. This is a fresh Bayesian bootstrap of the outcomes. The analysis rests on an exact identity: averaging any bounded proper loss under $\operatorname{Dir}(α)$ equals a discrete derivative of it...
| Authors | Pahan Dewasurendra |
|---|---|
| Primary category | cs.LG |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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