Adversarial Linear Contextual Bandits with Graph-Structured Side Observations
This work provides new algorithms for adversarial contextual bandits, which is relevant for researchers and practitioners working on online decision-making in social networks and similar graph-structured environments.
This paper addresses adversarial linear contextual bandits with graph-structured side observations, a setting where an agent chooses from K actions given a d-dimensional context and observes losses of chosen and neighboring actions. The authors propose two algorithms, EXP3-LGC-U and EXP3-LGC-IX, achieving regret bounds of O(sqrt((K+α(G)d)TlogK)) and O(sqrt(α(G)dTlogKlog(KT))) respectively, where α(G) is the average independence number of feedback graphs.
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 $\mathcal{O}(\sqrt{(K+α(G)d)T\log{K}})$ over the time horizon $T$, where $α(G)$ 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 $\mathcal{O}(\sqrt{α(G)dT\log{K}\log(KT)})$ for both directed as well as undirected feedback graphs. Numerical tests corroborate the efficiency of proposed algorithms.