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 alpha-vectors. We would like to find the best possible policy that can be expressed using a fixed number N of alpha-vectors. We call this the N-POMDP problem. The existing solver alpha-min approximately solves finite-horizon POMDPs with a controllable number of alpha-vectors. However alpha-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 alpha-min-2. These three algorithms are able to approximately solve N-POMDPs. Alpha-min-2-fast (heuristic) and alpha-min-2-p (with performance guarantees) are designed to complement an existing POMDP solver, while alpha-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.

Adaptive management is applied in conservation and natural resource management, and consists of making sequential decisions when the transition matrix is uncertain. Informally described as ’learning by doing’, this approach aims to trade off between decisions that help achieve the objective and decisions that will yield a better knowledge of the true transition matrix. When the true transition matrix is assumed to be an element of a finite set of possible matrices, solving a mixed observability Markov decision process (MOMDP) leads to an optimal trade-off but is very computationally demanding. Under the assumption (common in adaptive management) that the true transition matrix is stationary, we propose a polynomial-time algorithm to find a lower bound of the value function. In the corners of the domain of the value function (belief space), this lower bound is provably equal to the optimal value function. We also show that under further assumptions, it is a linear approximation of the optimal value function in a neighborhood around the corners. We evaluate the benefits of our approach by using it to initialize the solvers MO-SARSOP and Perseus on a novel computational sustainability problem and a recent adaptive management data challenge. Our approach leads to an improved initial value function and translates into significant computational gains for both solvers.