Solving stochastic dynamic programming models without transition matrices

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Abstract: Discrete dynamic programming, widely used in addressing optimization over time, suffers from the so-called curse of dimensionality, the exponential increase in problem size as the number of system variables increases. One method to reduce the computational resources required to find solutions is to avoid the use of state transition probability matrices, which grow in the square of the size of the state space. This can be done through the use of expected value (EV) functions, which compute the expectation of functions of the future state variables conditioned on current variables. Two ways that this leads to potential gains arise when the state transition can be broken into separate phases and when the transitions for different state variables are conditionally independent. Both of these situations arise in models that are used in natural resource management and are illustrated with several examples including the dyna mic reserves site selection problem, managing invasive species on a spatial network and managing wildlife harvests with multiple population stage classes. Efficiency gains include far lower memory requirements and orders of magnitude reductions in computing time.

Bio: Paul L. Fackler is a professor of agricultural and resource economics and associate professor of applied ecology at North Carolina State University and an internationally recognized teacher and scholar in the areas of decision analysis and computational methods. He co-authored a widely used textbook on the use of computational methods (Applied Computational Economics and Finance) along with the CompEcon Toolbox, a package of computer programs used in both teaching and research. The main focus of his research currently is the application of dynamic optimization tools to problems involving the management of natural resources. He is also the developer of the MDPSolve package for solving dynamic optimization problems. Among his published work in the area of resource management are the following papers:

Fred A. Johnson, Paul L. Fackler, G. Scott Boomer, Guthrie Zimmerman, Byron K. Williams, James D. Nichols and Robert M. Dorazio. (2016) State-Dependent Resource Harvesting with Lagged Information about System States. PLoS ONE.

Matthew J. MacLachlan, Michael R. Springborn and Paul L. Fackler. (2016) Learning about a moving target in resource management: Optimal Bayesian disease control. American Journal of Agricultural Economics.

Michele Baggio and Paul L. Fackler. (2016) Optimal management with reversible regime shifts. Journal of Economic Behavior and Organization.

Fackler PL, Pacifici K, Martin J, McIntyre C. (2014) Efficient Use of Information in Adaptive Management with an Application to Managing Recreation near Golden Eagle Nesting Sites. PLoS ONE.

Paul L. Fackler. (2014) Structural and Observational Uncertainty in Environmental and Natural Resource Management. International Review of Environmental and Resource Economics.

Fackler, Paul L. and Robert G. Haight. (2014) Monitoring as a Partially Observable Decision Problem. Resource and Energy Economics.

Paul L. Fackler and Krishna Pacifici. (2014) Addressing Structural and Observational Uncertainty in Resource Management. Journal of Environmental Management.

Lucile Marescot, Guillaume Chapron, Iadine Chadès, Paul L. Fackler, Christophe Duchamp, Eric Marboutin and Olivier Gimenez. (2013) Complex decisions made simple: a primer on stochastic dynamic programming. Methods in Ecology and Evolution.

Jaime A. Collazo, Paul L. Fackler, Krishna Pacifici, Thomas H. White Jr., Ivan Llerandi-Roman and Stephen J. Dinsmore. (2013) Optimal allocation of captive-reared Puerto Rican parrots: Decisions when divergent dynamics characterize managed populations. Journal of Wildlife Management.

Fackler, Paul L. (2012) Category count models for resource management. Methods in Ecology and Evolution.

Martin J,  Fackler PL, Nichols JD, Lubow BL, Runge, MC, McIntyre CL, Lubow BL, McCluskie MC, Schmutz JA. (2011) Adaptive-Management Framework for Optimal Control of Hiking Near Golden Eagles Nests in Denali National Park. Conservation Biology.

Martin J,  Nichols JD, Fackler PL, Lubow BL, Eaton MJ, Runge, MC, Stih BM, Langtimm CA. (2011) Structured decision making as a proactive approach to dealing with sea level rise in Florida. Climatic Change.