# Optimally Pacing Budget Spending and Learning

arXiv: https://arxiv.org/abs/2610.11074 · HTML: https://mlsanity.com/paper/2610.11074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 3 of 3)

- [Online Convex Optimization with Time-Varying Constraints](https://mlsanity.com/paper/1702.04783/) (2017)
- [Online optimization and regret guarantees for non-additive long-term constraints](https://mlsanity.com/paper/1602.05394/) (2016)
- [A New Benchmark for Online Learning with Budget-Balancing Constraints](https://mlsanity.com/paper/2503.14796/) (2025)

## Abstract (arXiv)

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 √log F+ √Tlog 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√log F) regret bounds when fractional allocation is allowed. This is the first algorithm we are aware of which can achieve o(√T) guarantees for such tasks.