Optimally Pacing Budget Spending and Learning
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Computer Science > Machine Learning
Title:Optimally Pacing Budget Spending and Learning
Abstract:We establish near-optimal regret bounds for budget-constrained online learning against arbitrary classes of budget-pacing experts in the adversarial setting. In particular, given any class of $F$ experts and a candidate budget pacing schedule, we provide a full-information algorithm which obtains regret $O(D \sqrt{\log F}+ \sqrt{T\log F})$ against all experts whose cumulative spending stays within distance $D$ of this schedule, matching lower bounds established by Braverman et al. (2025).
We additionally show that our technique extends to various problems in online resource allocation, where the learner gets to see the rewards and costs of the current options available to them, and establish $O(D\sqrt{\log F})$ regret bounds when fractional allocation is allowed. This is the first algorithm we are aware of which can achieve $o(\sqrt{T})$ guarantees for such tasks.
| Subjects: | Machine Learning (cs.LG); Computer Science and Game Theory (cs.GT) |
| Cite as: | arXiv:2610.11074 [cs.LG] |
| (or arXiv:2610.11074v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11074
arXiv-issued DOI via DataCite (pending registration)
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