Using Numerical Dynamic Programming to Compare Passive and Active Learning in the Adaptive Management of Nutrients in Shallow Lakes

This paper illustrates the use of dual/adaptive control methods to compare passive and active adaptive management decisions in the context of an ecosystem with a threshold effect. Using discrete-time dynamic programming techniques, we model optimal phosphorus loadings under both uncertainty about natural loadings and uncertainty regarding the critical level of phosphorus concentrations beyond which nutrient recycling begins. Active management is modeled by including the anticipated value of information (or learning) in the structure of the problem, and thus the agent can perturb the system (experiment), update beliefs, and learn about the uncertain parameter. Using this formulation, we define and value optimal experimentation both ex ante and ex post. Our simulation results show that experimentation is optimal over a large range of phosphorus concentration and belief space, though ex ante benefits are small in our example. Furthermore, realized benefits may critically depend on the true underlying parameters of the problem.