Censored Semi-Bandits for Resource Allocation

TL;DR

This paper introduces a novel resource allocation problem in censored semi-bandits, establishing its equivalence to MP-MAB and combinatorial semi-bandits, and proposes optimal algorithms validated through synthetic experiments.

Contribution

It formulates a new resource allocation problem with censored feedback, and derives optimal algorithms by leveraging equivalences to existing bandit models.

Findings

Proposed algorithms achieve near-optimal performance in synthetic tests.

Established theoretical equivalence to MP-MAB and combinatorial semi-bandits.

Validated effectiveness of algorithms through experiments.

Abstract

We consider the problem of sequentially allocating resources in a censored semi-bandits setup, where the learner allocates resources at each step to the arms and observes loss. The loss depends on two hidden parameters, one specific to the arm but independent of the resource allocation, and the other depends on the allocated resource. More specifically, the loss equals zero for an arm if the resource allocated to it exceeds a constant (but unknown) arm dependent threshold. The goal is to learn a resource allocation that minimizes the expected loss. The problem is challenging because the loss distribution and threshold value of each arm are unknown. We study this setting by establishing its `equivalence' to Multiple-Play Multi-Armed Bandits (MP-MAB) and Combinatorial Semi-Bandits. Exploiting these equivalences, we derive optimal algorithms for our problem setting using known algorithms for MP-MAB and Combinatorial Semi-Bandits. The experiments on synthetically generated data validate the performance guarantees of the proposed algorithms.