Path-planning with uncertainty: a simple model

There are already plenty of work on planning under uncertainty. Here we consider a simple model, where the uncertainty can be removed at a later time $T$ with different variations:

• A fixed deterministic $T$
• A random $T$ with a discrete distribution
• A random $T$ with a discrete, stage-different distribution
• A random $T$ with an exponential distribution

The stage-differently distributed $T$ can be illustrated by this motion picture. Assuming there are 4 possible target locations but only one of them is the true one. Starting from the source, we send out 3 drones to check each location while move to a better waypoint in the meantime.
Joint work with Adam Dhillon and Alexander Vladimirsky.