Bandits with Knapsacks beyond the Worst-Case [article]

Karthik Abinav Sankararaman, Aleksandrs Slivkins
2021 arXiv   pre-print
Bandits with Knapsacks (BwK) is a general model for multi-armed bandits under supply/budget constraints. While worst-case regret bounds for BwK are well-understood, we present three results that go beyond the worst-case perspective. First, we provide upper and lower bounds which amount to a full characterization for logarithmic, instance-dependent regret rates. Second, we consider "simple regret" in BwK, which tracks algorithm's performance in a given round, and prove that it is small in all
more » ... a few rounds. Third, we provide a general "reduction" from BwK to bandits which takes advantage of some known helpful structure, and apply this reduction to combinatorial semi-bandits, linear contextual bandits, and multinomial-logit bandits. Our results build on the BwK algorithm from , providing new analyses thereof.
arXiv:2002.00253v7 fatcat:modyv2tkpbbgpjrpuflfx62i3m