# Thompson Sampling For Stochastic Bandits with Graph Feedback

## TL;DR

This paper extends Thompson Sampling to stochastic bandit problems with unknown or changing graph feedback structures, providing theoretical regret guarantees and demonstrating superior empirical performance over UCB-based methods.

## Contribution

It introduces a novel Thompson Sampling algorithm for graph feedback in stochastic bandits, applicable even with unknown or dynamic graph structures, with proven regret bounds.

## Key findings

- Algorithm outperforms UCB-based methods on various real and simulated networks.
- Theoretical regret bounds linked to graph properties.
- Effective on diverse graph types including power law and social networks.

## Abstract

We present a novel extension of Thompson Sampling for stochastic sequential decision problems with graph feedback, even when the graph structure itself is unknown and/or changing. We provide theoretical guarantees on the Bayesian regret of the algorithm, linking its performance to the underlying properties of the graph. Thompson Sampling has the advantage of being applicable without the need to construct complicated upper confidence bounds for different problems. We illustrate its performance through extensive experimental results on real and simulated networks with graph feedback. More specifically, we tested our algorithms on power law, planted partitions and Erdo's-Renyi graphs, as well as on graphs derived from Facebook and Flixster data. These all show that our algorithms clearly outperform related methods that employ upper confidence bounds, even if the latter use more information about the graph.