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 feedback graph and where shifting to a new action incurs a fixed switching cost. We give two new algorithms for this problem in the informed setting. Our best algorithm achieves a pseudo-regret of Õ(?(G) ^{1 3} T ^{2 3} ), where ?(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.