Problem-dependent Regret Bounds for Online Learning with Feedback Graphs

This paper addresses the stochastic multi-armed bandit problem with an undirected feedback graph. We devise a UCB-based algorithm, UCB-NE, to provide a problem-dependent regret bound that depends on a clique covering. Our algorithm obtains regret which provably scales linearly with the clique covering number. Additionally, we provide problem-dependent regret bounds for a Thompson Sampling-based algorithm, TS-N, where again the bounds are linear in the clique covering number. Finally, we present experimental results to see how UCB-NE, TS-N, and a few related algorithms perform practically.