Three New Algorithms to Solve N-POMDPs

In many fields in computational sustainability, applications of POMDPs are inhibited by the complexity of the optimal solution. One way of delivering simple solutions is to represent the policy with a small number of α-vectors. We would like to find the best possible policy that can be expressed using a fixed number N of α-vectors. We call this the N-POMDP problem. The existing solver α-min approximately solves finite-horizon POMDPs with a controllable number of α-vectors. However α-min is a greedy algorithm without performance guarantees, and it is rather slow. This paper proposes three new algorithms, based on a general approach that we call α-min-2. These three algorithms are able to approximately solve N-POMDPs. α-min-2-fast (heuristic) and α-min-2-p (with performance guarantees) are designed to complement an existing POMDP solver, while α-min-2-solve (heuristic) is a solver itself. Complexity results are provided for each of the algorithms, and they are tested on well-known benchmarks. These new algorithms will help users to interpret solutions to POMDP problems in computational sustainability.