THEORY

REINFORCEMENT LEARNING

Bandits with Knapsacks beyond the Worst-Case Analysis

November 12, 2021

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 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 Agrawal and Devanur (2014), providing new analyses thereof.

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AUTHORS

Written by

Karthik Abinav Sankararaman

Aleksandrs Slivkins

Publisher

NeurIPS

Research Topics

Theory

Reinforcement Learning

Core Machine Learning

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