Shortest path optimization under limited information

The problem of finding an optimal path in an uncertain graph arises in numerous applications, including network routing, path-planning for vehicles, and the control of finite-state systems. While techniques in robust and stochastic programming can be employed to compute, respectively, worst-case and average-optimal solutions to the shortest-path problem, we consider an alternative problem where the agent that traverses the graph can request limited information about the graph before choosing a path to traverse. In this paper, we define and quantify a notion of information that is compatible to this performance-based framework, bound the performance of the agent subject to a bound on the capacity of the information it can request, and present algorithms for optimizing information.