POMDPs for sustainable fishery management

The challenge of sustainable fishery management is to design harvest policies that attain the dual objectives of: (a) protecting the species from over fishing, and (b) ensuring adequate economic return to fishers. It is clear that a suitable compromise between these two, conflicting, objectives must be achieved. However, a major difficulty stems from the need to deal with various sources of uncertainty associated with the fluctuations of the population, such as sea-surface temperature, pollution, or levels of nutrients. This is further complicated by the uncertainties associated with the effects of the management decisions and fishing pressure. Partially Observable Markov Decision Processes (POMDPs) provide a natural mathematical framework for incorporating these uncertainties in the decision making process. This was already recognised by several authors. However, the promise of POMDPs has not yet been realised because they are provably computationally hard to solve in general, and for many years were considered to be solvable only for toy problems. In addition, the underlying dynamics of fish populations are normally described by deterministic difference or differential equations and it is not entirely clear how these should be incorporated into the stochastic dynamics of POMDPs. This paper summarizes a, still preliminary, study that tackles both of the above problems. In particular, the computational complexity problem is tackled with the help of suitable discretization of state and action spaces and DESPOT; a state-of-the-art POMDP solver. In addition, the deterministic dynamics of the widely used Beverton-Holt model are modified to incorporate stochasticity in both the proliferation rate and in the observations based on catch and the outputs of the latter model. The resulting POMDP formulation takes into account some of the uncertainties in managing fisheries, and shows that an adaptive management policy can be more advantageous than a simple fixed action policy. We also report on experiments with various modelling choices and their effects on the resulting policy. Finally, recognising that POMDP policies are sometimes hard to interpret, we demonstrate that our adaptive management policy possesses an attractive feedback (or closed-loop) structure. Namely, the actions selected by that policy depend on the current expected biomass of the harvested species. Effectively, the policy maps the current expected biomass to a decision to use certain harvest levels in prescribed proportions. Naturally, when the expected biomass is low the more conservative (i.e., lower) harvest actions are preferred. On the other hand, when the expected biomass is high, actions corresponding to higher harvest levels are selected. Nonetheless, the most intensive (i.e., greedy) harvest levels are never selected because of the sustainability concerns.