Adversarial Linear Contextual Bandits with Graph-Structured Side Observations

TL;DR

This paper introduces two algorithms for adversarial graphical contextual bandits that incorporate side observations structured as feedback graphs, achieving near-optimal regret bounds in social network applications.

Contribution

The paper develops two efficient algorithms based on EXP3 for adversarial graphical contextual bandits with theoretical regret guarantees under mild conditions.

Findings

Algorithms achieve regret bounds of order O(√((K+α(G)d)T log K)) and O(√(α(G)dT log K log(KT)))

Numerical tests confirm the efficiency of the proposed algorithms

Models applications in social networks with context and graph-structured side observations

Abstract

This paper studies the adversarial graphical contextual bandits, a variant of adversarial multi-armed bandits that leverage two categories of the most common side information: \emph{contexts} and \emph{side observations}. In this setting, a learning agent repeatedly chooses from a set of $K$ actions after being presented with a $d$-dimensional context vector. The agent not only incurs and observes the loss of the chosen action, but also observes the losses of its neighboring actions in the observation structures, which are encoded as a series of feedback graphs. This setting models a variety of applications in social networks, where both contexts and graph-structured side observations are available. Two efficient algorithms are developed based on \texttt{EXP3}. Under mild conditions, our analysis shows that for undirected feedback graphs the first algorithm, \texttt{EXP3-LGC-U}, achieves the regret of order $\mathcal{O}(\sqrt{(K+\alpha(G)d)T\log{K}})$ over the time horizon $T$, where $\alpha(G)$ is the average \emph{independence number} of the feedback graphs. A slightly weaker result is presented for the directed graph setting as well. The second algorithm, \texttt{EXP3-LGC-IX}, is developed for a special class of problems, for which the regret is reduced to $\mathcal{O}(\sqrt{\alpha(G)dT\log{K}\log(KT)})$ for both directed as well as undirected feedback graphs. Numerical tests corroborate the efficiency of proposed algorithms.