Ising bandits with side information

We develop an online learning algorithm for bandits on a graph with side information where there is an underlying Ising distribution over the vertices at low temperatures. We are motivated from practical settings where the graph state in a social or a computer hosts network (potentially) changes at every trial; intrinsically partitioning the graph thus requiring the learning algorithm to play the bandit from the current partition. Our algorithm essentially functions as a two stage process. In the first stage it uses "minimum-cut" as the regularity measure to compute the state of the network by using the side label received and acting as a graph classifier. The classifier internally uses a polynomial time linear programming relaxation technique that incorporates the known information to predict the unknown states. The second stage ensures that the bandits are sampled from the appropriate partition of the graph with the potential for exploring the other part. We achieve this by running the adversarial multi armed bandit for the edges in the current partition while exploring the "cut" edges. We empirically evaluate the strength of our approach through synthetic and real world datasets. We also indicate the potential for a linear time exact algorithm for calculating the max-flow as an alternative to the linear programming relaxation, besides promising bounded mistakes/regret in the number of times the "cut" changes.