Adversarial Linear Contextual Bandits with Graph-Structured Side Observations

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