Poster

Bandits with Knapsacks beyond the Worst Case

Karthik Abinav Sankararaman · Aleksandrs Slivkins

Keywords: [ Theory ] [ Online Learning ] [ Bandits ]

[ Abstract ]
[ OpenReview
Tue 7 Dec 8:30 a.m. PST — 10 a.m. PST

Abstract:

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 but a few rounds. Third, we provide a "generalreduction" 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 prior work, providing new analyses thereof.

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