  We study multi-armed bandit problems with graph feedback, in which the
decision maker is allowed to observe the neighboring actions of the chosen
action, in a setting where the graph may vary over time and is never fully
revealed to the decision maker. We show that when the feedback graphs are
undirected, the original Thompson Sampling achieves the optimal (within
logarithmic factors) regret $\tilde{O}\left(\sqrt{\beta_0(G)T}\right)$ over
time horizon $T$, where $\beta_0(G)$ is the average independence number of the
latent graphs. To the best of our knowledge, this is the first result showing
that the original Thompson Sampling is optimal for graphical bandits in the
undirected setting. A slightly weaker regret bound of Thompson Sampling in the
directed setting is also presented. To fill this gap, we propose a variant of
Thompson Sampling, that attains the optimal regret in the directed setting
within a logarithmic factor. Both algorithms can be implemented efficiently and
do not require the knowledge of the feedback graphs at any time.

Machine Learning;Artificial Intelligence;Machine Learning