Bandits with Feedback Graphs and Switching Costs

We study the adversarial multi-armed bandit problem where the learner is supplied with partial observations modeled by a \emph{feedback graph} and where shifting to a new action incurs a fixed \emph{switching cost}. We give two new algorithms for this problem in the informed setting. Our best algorithm achieves a pseudo-regret of $\tilde O(\gamma(G)^{\frac{1}{3}}T^{\frac{2}{3}})$, where $\gamma(G)$ is the domination number of the feedback graph. This significantly improves upon the previous best result for the same problem, which was based on the independence number of $G$. We also present matching lower bounds for our result that we describe in detail. Finally, we give a new algorithm with improved policy regret bounds when partial counterfactual feedback is available.