Optimal Lower Bounds for Online Multicalibration
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910161233248256 |
|---|---|
| author | Collina, Natalie Lu, Jiuyao Noarov, Georgy Roth, Aaron |
| author_facet | Collina, Natalie Lu, Jiuyao Noarov, Georgy Roth, Aaron |
| contents | We prove tight lower bounds for online multicalibration, establishing an information-theoretic separation from marginal calibration.
In the general setting where group functions can depend on both context and the learner's predictions, we prove an $Ω(T^{2/3})$ lower bound on expected multicalibration error using just three disjoint binary groups. This matches the upper bounds of Noarov et al. (2025) up to logarithmic factors and exceeds the $O(T^{2/3-\varepsilon})$ upper bound for marginal calibration (Dagan et al., 2025), thereby separating the two problems.
We then turn to lower bounds for the more difficult case of group functions that may depend on context but not on the learner's predictions. In this case, we establish an $\widetildeΩ(T^{2/3})$ lower bound for online multicalibration via an $O(\log^3 T)$-sized group family constructed from an orthonormal basis, again matching upper bounds up to logarithmic factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Lower Bounds for Online Multicalibration Collina, Natalie Lu, Jiuyao Noarov, Georgy Roth, Aaron Machine Learning Statistics Theory We prove tight lower bounds for online multicalibration, establishing an information-theoretic separation from marginal calibration. In the general setting where group functions can depend on both context and the learner's predictions, we prove an $Ω(T^{2/3})$ lower bound on expected multicalibration error using just three disjoint binary groups. This matches the upper bounds of Noarov et al. (2025) up to logarithmic factors and exceeds the $O(T^{2/3-\varepsilon})$ upper bound for marginal calibration (Dagan et al., 2025), thereby separating the two problems. We then turn to lower bounds for the more difficult case of group functions that may depend on context but not on the learner's predictions. In this case, we establish an $\widetildeΩ(T^{2/3})$ lower bound for online multicalibration via an $O(\log^3 T)$-sized group family constructed from an orthonormal basis, again matching upper bounds up to logarithmic factors. |
| title | Optimal Lower Bounds for Online Multicalibration |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2601.05245 |