Algorithms improve pacing of budgets in online decision making
Optimally Pacing Budget Spending and Learning
Machine LearningComputer Science and Game Theory
Summary
Managing how to spend a fixed budget over time while learning which choices work best is a tricky problem. The authors present methods that nearly match the best possible accuracy for this challenge, even when facing unpredictable conditions. Their techniques also apply when resources can be partially allocated, improving efficiency. This advances how decisions can be made to balance spending plans and learning rewards.
What this means in practice
- •For advertising campaign managers: Plan and adjust digital ad spending in real-time to match budget schedules while learning which placements yield the best results.
- •For cloud resource schedulers: Allocate computing resources dynamically under budget constraints to optimize usage based on observed task costs and rewards.
Authors
Mark Braverman, Jingyi Liu, Jieming Mao, Jon Schneider, Eric Xue
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.