Optimal Resource Allocation with Semi-Bandit Feedback

Tor Lattimore, Koby Crammer, Csaba Szepesvari
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:126-135, 2014.

Abstract

We study a sequential resource allocation prob- lem involving a fixed number of recurring jobs. At each time-step the manager should distribute available resources among the jobs in order to maximise the expected number of completed jobs. Allocating more resources to a given job in- creases the probability that it completes, but with a cut-off. Specifically, we assume a linear model where the probability increases linearly until it equals one, after which allocating additional re- sources is wasteful. We assume the difficulty of each job is unknown and present the first algo- rithm for this problem and prove upper and lower bounds on its regret. Despite its apparent sim- plicity, the problem has a rich structure: we show that an appropriate optimistic algorithm can im- prove its learning speed dramatically beyond the results one normally expects for similar problems as the problem becomes resource-laden.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-lattimore14a, title = {Optimal Resource Allocation with Semi-Bandit Feedback}, author = {Lattimore, Tor and Crammer, Koby and Szepesvari, Csaba}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {126--135}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/lattimore14a/lattimore14a.pdf}, url = {https://proceedings.mlr.press/r12/lattimore14a.html}, abstract = {We study a sequential resource allocation prob- lem involving a fixed number of recurring jobs. At each time-step the manager should distribute available resources among the jobs in order to maximise the expected number of completed jobs. Allocating more resources to a given job in- creases the probability that it completes, but with a cut-off. Specifically, we assume a linear model where the probability increases linearly until it equals one, after which allocating additional re- sources is wasteful. We assume the difficulty of each job is unknown and present the first algo- rithm for this problem and prove upper and lower bounds on its regret. Despite its apparent sim- plicity, the problem has a rich structure: we show that an appropriate optimistic algorithm can im- prove its learning speed dramatically beyond the results one normally expects for similar problems as the problem becomes resource-laden.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Optimal Resource Allocation with Semi-Bandit Feedback %A Tor Lattimore %A Koby Crammer %A Csaba Szepesvari %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-lattimore14a %I PMLR %P 126--135 %U https://proceedings.mlr.press/r12/lattimore14a.html %V R12 %X We study a sequential resource allocation prob- lem involving a fixed number of recurring jobs. At each time-step the manager should distribute available resources among the jobs in order to maximise the expected number of completed jobs. Allocating more resources to a given job in- creases the probability that it completes, but with a cut-off. Specifically, we assume a linear model where the probability increases linearly until it equals one, after which allocating additional re- sources is wasteful. We assume the difficulty of each job is unknown and present the first algo- rithm for this problem and prove upper and lower bounds on its regret. Despite its apparent sim- plicity, the problem has a rich structure: we show that an appropriate optimistic algorithm can im- prove its learning speed dramatically beyond the results one normally expects for similar problems as the problem becomes resource-laden. %Z Reissued by PMLR on 04 October 2026.
APA
Lattimore, T., Crammer, K. & Szepesvari, C.. (2014). Optimal Resource Allocation with Semi-Bandit Feedback. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:126-135 Available from https://proceedings.mlr.press/r12/lattimore14a.html. Reissued by PMLR on 04 October 2026.

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