Hindsight is Only 50/50: Unsuitability of MDP based Approximate POMDP Solvers for Multi-resolution Information Gathering

Partially Observable Markov Decision Processes (POMDPs) offer an elegant framework to model sequential decision making in uncertain environments. Solving POMDPs online is an active area of research and given the size of real-world problems approximate solvers are used. Recently, a few approaches have been suggested for solving POMDPs by using MDP solvers in conjunction with imitation learning. MDP based POMDP solvers work well for some cases, while catastrophically failing for others. The main failure point of such solvers is the lack of motivation for MDP solvers to gain information, since under their assumption the environment is either already known as much as it can be or the uncertainty will disappear after the next step. However for solving POMDP problems gaining information can lead to efficient solutions. In this paper we derive a set of conditions where MDP based POMDP solvers are provably sub-optimal. We then use the well-known tiger problem to demonstrate such sub-optimality. We show that multi-resolution, budgeted information gathering cannot be addressed using MDP based POMDP solvers. The contribution of the paper helps identify the properties of a POMDP problem for which the use of MDP based POMDP solvers is inappropriate, enabling better design choices.