Open Problem: Online Sabotaged Shortest Path

There has been much work on extending the prediction with expert advice methodology to the case when experts are composed of components and there are combinatorially many such experts. One of the core examples is the Online Shortest Path problem where the components are edges and the experts are paths. In this note we revisit this online routing problem in the case where in each trial some of the edges or components are sabotaged / blocked. In the vanilla expert setting a known method can solve this extension where experts are now awake or asleep in each trial. We ask whether this technology can be upgraded efficiently to the case when at each trial every component can be awake or asleep. It is easy get to get an initial regret bound by using combinatorially many experts. However it is open whether there are efficient algorithms achieving the same regret.