English

Chasing Convex Functions with Long-term Constraints

Data Structures and Algorithms 2024-07-15 v2 Machine Learning

Abstract

We introduce and study a family of online metric problems with long-term constraints. In these problems, an online player makes decisions xt\mathbf{x}_t in a metric space (X,d)(X,d) to simultaneously minimize their hitting cost ft(xt)f_t(\mathbf{x}_t) and switching cost as determined by the metric. Over the time horizon TT, the player must satisfy a long-term demand constraint tc(xt)1\sum_{t} c(\mathbf{x}_t) \geq 1, where c(xt)c(\mathbf{x}_t) denotes the fraction of demand satisfied at time tt. Such problems can find a wide array of applications to online resource allocation in sustainable energy/computing systems. We devise optimal competitive and learning-augmented algorithms for the case of bounded hitting cost gradients and weighted 1\ell_1 metrics, and further show that our proposed algorithms perform well in numerical experiments.

Keywords

Cite

@article{arxiv.2402.14012,
  title  = {Chasing Convex Functions with Long-term Constraints},
  author = {Adam Lechowicz and Nicolas Christianson and Bo Sun and Noman Bashir and Mohammad Hajiesmaili and Adam Wierman and Prashant Shenoy},
  journal= {arXiv preprint arXiv:2402.14012},
  year   = {2024}
}

Comments

Accepted to ICML 2024. 31 pages, 12 figures

R2 v1 2026-06-28T14:56:04.822Z