What makes some POMDP problems easy to approximate?

Point-based algorithms have been surprisingly successful in computing approximately optimal solutions for partially observable Markov decision processes (POMDPs) in high dimensional belief spaces. In this work, we seek to understand the belief-space properties that allow some POMDP problems to be approximated efficiently and thus help to explain the point-based algorithms’ success often observed in the experiments. We show that an approximately optimal POMDP solution can be computed in time polynomial in the covering number of a reachable belief space, which is the subset of the belief space reachable from a given belief point. We also show that under the weaker condition of having a small covering number for an optimal reachable space, which is the subset of the belief space reachable under an optimal policy, computing an approximately optimal solution is NP-hard. However, given a suitable set of points that “cover” an optimal reachable space well, an approximate solution can ...

• Type: Conference
• Year: 2007
• Where: NIPS
• Authors: David Hsu, Wee Sun Lee, Nan Rong
• Keywords: Belief Space, Covering Number, Information Technology, NIPS 2007, Optimal Reachable Space