# Thresholding Graph Bandits with GrAPL

## TL;DR

This paper introduces Thresholding Graph Bandits, a new online decision-making framework that leverages graph-based similarities among arms to efficiently identify those exceeding a reward threshold, supported by the GrAPL algorithm.

## Contribution

The paper proposes the GrAPL algorithm for thresholding graph bandits, effectively utilizing graph structure and reward homophily for improved decision-making.

## Key findings

- GrAPL effectively exploits graph structure and reward homophily.
- Theoretical analysis confirms the algorithm's efficiency.
- Experimental results on synthetic and real data validate the approach.

## Abstract

In this paper, we introduce a new online decision making paradigm that we call Thresholding Graph Bandits. The main goal is to efficiently identify a subset of arms in a multi-armed bandit problem whose means are above a specified threshold. While traditionally in such problems, the arms are assumed to be independent, in our paradigm we further suppose that we have access to the similarity between the arms in the form of a graph, allowing us gain information about the arm means in fewer samples. Such settings play a key role in a wide range of modern decision making problems where rapid decisions need to be made in spite of the large number of options available at each time. We present GrAPL, a novel algorithm for the thresholding graph bandit problem. We demonstrate theoretically that this algorithm is effective in taking advantage of the graph structure when available and the reward function homophily (that strongly connected arms have similar rewards) when favorable. We confirm these theoretical findings via experiments on both synthetic and real data.