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A primer on partially observable Markov decision processes (POMDPs)

METHODS IN ECOLOGY AND EVOLUTION 2021年第11期12卷 2058-2072页

作者： Chades, Iadine Pascal, Luz V. Nicol, Sam Fletcher, Cameron S. Ferrer-Mestres, Jonathan CSIRO Dutton Pk Qld Australia ENSTA Palaiseau France CSIRO Atherton Qld Australia

Partially observable Markov decision processes (POMDPs) are a convenient mathematical model to solve sequential decision-making problems under imperfect observations. Most notably for ecologists, POMDPs have helped solve the trade-offs between investing in management or surveillance and, more recently, to optimise adaptive management problems. Despite an increasing number of applications in ecology and natural resources, POMDPs are still poorly understood. The complexity of the mathematics, the inaccessibility of POMDP solvers developed by the Artificial Intelligence (AI) community, and the lack of introductory material are likely reasons for this. We propose to bridge this gap by providing a primer on POMDPs, a typology of case studies drawn from the literature, and a repository of POMDP problems. We explain the steps required to define a POMDP when the state of the system is imperfectly detected (state uncertainty) and when the dynamics of the system are unknown (model uncertainty). We provide input files and solutions to a selected number of problems, reflect on lessons learned applying these models over the last 10 years and discuss future research required on interpretable AI. Partially observable Markov decision processes are powerful decision models that allow users to make decisions under imperfect observations over time. This primer will provide a much-needed entry point to ecologists.

关键词： AI decisions partially observable Markov decision processes stochastic dynamic programming uncertainty

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Optimal Strategies for Managing Wildlife Harvest Under System Change

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JOURNAL OF WILDLIFE MANAGEMENT 2021年第5期85卷 847-854页

作者： Tucker, Anna M. Runge, Michael C. US Geol Survey Eastern Ecol Sci Ctr Patuxent Res Refuge 12100 Beech Forest Rd Laurel MD 20708 USA Iowa State Univ Dept Nat Resources Ecol & Management US Geol Survey Iowa Cooperat Fish & Wildlife Res Unit Ames IA 50011 USA

Wildlife populations are experiencing shifting dynamics due to climate and landscape change. Management policies that fail to account for non-stationary dynamics may fail to achieve management objectives. We establish a framework for understanding optimal strategies for managing a theoretical harvested population under non-stationarity. Building from harvest theory, we develop scenarios representing changes in population growth rate (r) or carrying capacity (K) and derive time-dependent optimal harvest policies using stochastic dynamic programming. We then evaluate the cost of falsely assuming stationarity by comparing the outcomes of forward projections in which either the optimal policy or a stationary policy is applied. When K declines over time, the stationary policy leads to an underharvest of the population, resulting in less harvest over the short term but leaving the population in a higher-value state. When r declines over time, the stationary policy leads to overharvest, resulting in greater harvest returns in the short term but leaving the population in a lower and potentially more vulnerable state. This work demonstrates the basic properties of time-dependent harvest management and provides a framework for evaluating the many outstanding questions about optimal management strategies under climate change. Published 2021. This article is a U.S. Government work and is in the public domain in the USA.

关键词： climate change harvest management non‐ stationary dynamics stochastic dynamic programming

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Modeling the impacts of a changing and disturbed environment on an endangered beluga whale population

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ECOLOGICAL MODELLING 2023年第1期483卷

作者： McHuron, Elizabeth A. Castellote, Manuel Boor, Himes Shelden, Kim E. W. Warlick, Amanda J. McGuire, Tamara L. Wade, Paul R. Goetz, Kimberly T. Univ Washington Cooperat Inst Climate Ocean & Ecosyst Studies Seattle WA 98105 USA Alaska Fisheries Sci Ctr Natl Marine Fisheries Serv Marine Mammal Lab Seattle WA 98115 USA Montana State Univ Ecol Dept Bozeman MT 59717 USA Univ Washington Sch Aquat & Fishery Sci Seattle WA 98115 USA Cook Inlet Beluga Whale Photoid Project Anchorage AK 99515 USA

Climate change and disturbance from human activities are key threats facing many wildlife populations worldwide. The ability to quantify the effects of such threats on individual health and population dynamics is critical for effective management and conservation. We used stochastic dynamic programming (SDP), a method for implementing state-dependent life history theory, to explore the impacts of changes in prey availability and anthropogenic disturbance on survival and reproductive success of Cook Inlet belugas (Delphinapterus leucas, CIB), an endangered and isolated population in decline. We predicted behavioral decisions (whether to forage, travel to a new location, or rest) of pregnant CIBs within a spatially and seasonally dynamic prey landscape. We used those decisions to explore time-activity budgets and spatial use under a variety of hypothetical environ-mental scenarios and estimate the resulting impacts on body condition and vital rates. In all scenarios, foraging activity was highest during summer to capitalize on abundant prey, which in the model was assumed to be eulachon (Thaleichthys pacificus) and salmonids (Oncorhynchus spp.). This resulted in large increases in blubber reserves that pregnant CIBs relied on during October to April when prey was assumed to be less abundant. Prey availability outside of summer months was still critical, as it either exacerbated or buffered against reductions in prey availability during summer months. Spatial predictions of habitat use indicated that pregnant CIBs should forage in areas used historically that now appear to be abandoned, suggesting that prey availability alone is unlikely to explain the recent range contraction of CIBs to upper Cook Inlet. Reductions in prey availability from late spring to early fall adversely affected vital rates, but intermittent disturbances that resulted in lost foraging opportunities, such as those caused by anthropogenic activities during the ice-free season, had little impact on

关键词： Bioenergetics Cook Inlet Delphinapterus leucas Population consequence of disturbance Prey availability stochastic dynamic programming

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A Guide on Solving Non-convex Consumption-Saving Models

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COMPUTATIONAL ECONOMICS 2021年第3期58卷 747-775页

作者： Druedahl, Jeppe Univ Copenhagen Dept Econ CEBI Oster Farimagsgade 5Bldg 26 DK-1353 Copenhagen K Denmark

Consumption-saving models with adjustment costs or discrete choices are typically hard to solve numerically due to the presence of non-convexities. This paper provides a number of tools to speed up the solution of such models. Firstly, I use that many consumption models have a nesting structure implying that the continuation value can be efficiently pre-computed and the consumption choice solved separately before the remaining choices. Secondly, I use that an endogenous grid method extended with an upper envelope step can be used to solve efficiently for the consumption choice. Thirdly, I use that the required pre-computations can be optimized by a novel loop reordering when interpolating the next-period value function. As an illustrative example, I solve a model with non-durable consumption and durable consumption subject to adjustment costs. Combining the provided tools, the model is solved almost 50 times faster than with standard value function iteration for a given level of accuracy. Software is provided in both Python and C++.

关键词： Endogenous grid method Post-decision states stochastic dynamic programming Continuous and discrete choices Occasionally binding constraints

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Economically optimal hydropower development with uncertain climate change

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JOURNAL OF HYDROLOGY 2023年第PartA期627卷

作者： Liu, Benxi Liao, Shengli Lund, Jay R. Jin, Xiaoyu Cheng, Chuntian Dalian Univ Technol Inst Hydropower & Hydroinformat Dalian 116024 Peoples R China Univ Calif Davis Dept Civil & Environm Engn Davis CA 95616 USA Dalian Univ Technol Inst Hydropower & Hydroinformat Room 5183 Lab Bldg2 Linggong Rd Dalian 116024 Liaoning Peoples R China

Climate change affects the planning, construction, operation and management of hydropower plants in various ways. Evaluating hydropower generation with nonstationary climate changes is important for planning electric power infrastructure development. For a new hydropower plant with climate change, specifying too large a reservoir may result in excessive investment if the future becomes drier, while too small a reservoir may cause insufficient utilization of hydropower resources. Whether to build a new hydropower station at once or build it dynamically in stages over time is challenged by uncertainty in future conditions. This study proposes a planning method for developing a flexible hydropower construction schedule to adapt to long-term uncertain hydrology with climate changes. Projected uncertain nonstationary hydrology scenarios were developed first, and Bayes' theorem is used to update the probability of each scenario based on observed hydrologic conditions over time. A profit maximization model integrates stochastic dynamic programming and linear programming for a cascade hydropower system to evaluate hydropower plant expansion and how to build it dynamically with uncertain nonstationary climate conditions. In this, stochastic dynamic programming evaluates and prescribes inter-stage reservoir upgrades and linear programming prescribes inner-stage hydroelectric power generation. The case study of Jinsha cascade hydropower system in China's Yunnan province illustrates the method. The intensity and trend of climate change effects on streamflow directly affect the optimized results. If streamflow decreases in the future, the best strategy is to build a small reservoir initially, without future changes. If streamflow increases in the future, it is better to build a small reservoir first, and gradually increase capacity according to observed changes in streamflow and economies of scale in capacity construction. If there is no clear trend in streamflow change, it is a

关键词： Nonstationary climate change Hydropower plant planning Bayes ' theorem stochastic dynamic programming

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Predicting resilience of migratory birds to environmental change

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2024年第19期121卷 1页

作者： Lisovski, Simeon Hoye, Bethany J. Conklin, Jesse R. Battley, Phil F. Fuller, Richard A. Gosbell, Ken B. Klaassen, Marcel Lee, Chengfa Benjamin Murray, Nicholas J. Bauer, Silke Alfred Wegener Inst Sect Polar Terr Environm Syst Helmholtz Ctr Polar & Marine Res D-14473 Potsdam Germany Univ Wollongong Sch Earth Atmospher & Life Sci Wollongong NSW 2522 Australia Univ Groningen Groningen Inst Evolutionary Life Sci Conservat Ecol Grp NL-9700 Groningen Netherlands Massey Univ Zool & Ecol Grp Palmerston North 4442 New Zealand Univ Queensland Sch Environm Brisbane Qld 4072 Australia Victorian Wader Study Grp Blackburn Vic 3130 Australia Deakin Univ Ctr Integrat Ecol Sch Life & Environm Sci Geelong Vic 3217 Australia Remote Sensing Technol Inst German Aerosp Ctr D-12489 Berlin Germany Univ Wurzburg Dept Remote Sensing EAGLE M Sc Program D-97074 Wurzburg Germany James Cook Univ Coll Sci & Engn Townsville Qld 4811 Australia Fed Res Inst WSL CH-8903 Birmensdorf Switzerland Swiss Ornithol Inst Dept Bird Migrat CH-6204 Sempach Switzerland Univ Amsterdam Inst Biodivers & Ecosyst Dynam NL-1090 GE Amsterdam Netherlands Swiss Fed Inst Technol Dept Environm Syst Sci CH-8902 Zurich Switzerland

The pace and scale of environmental change represent major challenges to many organisms. Animals that move long distances, such as migratory birds, are especially vulnerable to change since they need chains of intact habitat along their migratory routes. Estimating the resilience of such species to environmental changes assists in targeting conservation efforts. We developed a migration modeling framework to predict past (1960s), present (2010s), and future (2060s) optimal migration strategies across five shorebird species (Scolopacidae) within the East Asian- Australasian Flyway, which has seen major habitat deterioration and loss over the last century, and compared these predictions to empirical tracks from the present. Our model captured the migration strategies of the five species and identified the changes in migrations needed to respond to habitat deterioration and climate change. Notably, the larger species, with single or few major stopover sites, need to establish new migration routes and strategies, while smaller species can buffer habitat loss by redistributing their stopover areas to novel or less - used sites. Comparing model predictions with empirical tracks also indicates that larger species with the stronger need for adaptations continue to migrate closer to the optimal routes of the past, before habitat deterioration accelerated. Our study not only quantifies the vulnerability of species in the face of global change but also explicitly reveals the extent of adaptations required to sustain their migrations. This modeling framework provides a tool for conservation planning that can accommodate the future needs of

关键词： global change biology optimal migration habitat deterioration avian migration stochastic dynamic programming

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Predicting the population consequences of acoustic disturbance, with application to an endangered gray whale population

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ECOLOGICAL APPLICATIONS 2021年第8期31卷 1-21页

作者： McHuron, Elizabeth A. Aerts, Lisanne Gailey, Glenn Sychenko, Olga Costa, Daniel P. Mangel, Marc Schwarz, Lisa K. Univ Calif Santa Cruz Inst Marine Sci Santa Cruz CA 95064 USA Univ Calif Santa Cruz Dept Ecol & Evolutionary Biol Santa Cruz CA 95064 USA LAMA Ecol Anchorage AK 99502 USA Cetacean EcoSyst Res Lacey WA 98516 USA Univ Bergen Dept Biol Theoret Ecol Grp N-9020 Bergen Norway Univ Washington Puget Sound Inst Tacoma WA 98402 USA Univ Washington Cooperat Inst Climate Ocean & Ecosyst Studies Seattle WA 98195 USA

Acoustic disturbance is a growing conservation concern for wildlife populations because it can elicit physiological and behavioral responses that can have cascading impacts on population dynamics. State-dependent behavioral and life history models implemented via stochastic dynamic programming (SDP) provide a natural framework for quantifying biologically meaningful population changes resulting from disturbance by linking environment, physiology, and metrics of fitness. We developed an SDP model using the endangered western gray whale (Eschrichtius robustus) as a case study because they experience acoustic disturbance on their summer foraging grounds. We modeled the behavior and physiological dynamics of pregnant females as they arrived on the feeding grounds and predicted the probability of female and offspring survival, with and without acoustic disturbance and in the presence/absence of high prey availability. Upon arrival in mid-May, pregnant females initially exhibited relatively random behavior before they transitioned to intensive feeding that resulted in continual fat mass gain until departure. This shift in behavior co-occurred with a change in spatial distribution;early in the season, whales were more equally distributed among foraging areas with moderate to high energy availability, whereas by mid-July whales transitioned to predominate use of the location that had the highest energy availability. Exclusion from energy-rich offshore areas led to reproductive failure and in extreme cases, mortality of adult females that had lasting impacts on population dynamics. Simulated disturbances in nearshore foraging areas had little to no impact on female survival or reproductive success at the population level. At the individual level, the impact of disturbance was unequally distributed across females of different lengths, both with respect to the number of times an individual was disturbed and the impact of disturbance on vital rates. Our results highlight the su

关键词： bioenergetics Eschrichtius robustus individual-based model population consequences of disturbance stochastic dynamic programming

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Optimal investment strategy for DC pension plan with inflation risk under the hybrid stochastic volatility model

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SYSTEMS SCIENCE & CONTROL ENGINEERING 2023年第1期11卷

作者： Shao, Yanyu Xia, Dengfeng Fei, Weiyin Anhui Polytech Univ Sch Math Phys & Finance Anhui Peoples R China

In this paper, we investigate an optimal investment strategy for defined-contribution (DC) pension plan under hybrid stochastic volatility (Heston-Hull-White) model, taking account of the inflation risk and the stochastic salary. The fund wealth is invested in financial market consisting of a risk-free asset, an inflation-indexed bond and a stock with hybrid Heston-Hull-White model. The goal of the pension fund manager is to maximize the expected utility of the terminal real wealth. We derive the Hamilton-Jacobi-Bellman (HJB) equation through the dynamic programming principle, under the constant relative risk aversion (CRRA) utility function, the optimal investment strategy is obtained. Finally, a numerical example is presented to characterize the impacts of financial parameters on the optimal investment strategy.

关键词： DC pension plan stochastic dynamic programming hybrid stochastic volatility inflation risk stochastic salary

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A stochastic dynamic programming model for valuing exclusivity from encroachment in franchising

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2012年第2期63卷 151-159页

作者： Tikoo, S. Liu, S. Nair, S. K. SUNY Coll New Paltz Sch Business New Paltz NY 12561 USA Univ Connecticut Storrs CT USA

Valuing territorial exclusivity in franchising is difficult because of the uncertainty associated with variables such as future franchise sales and brand strength. We present a stochastic dynamic programming model to value the exclusivity option from the perspective of both the franchisor and the franchisee. When there is positive value to the franchisor of including the exclusivity option in the contract, and to the franchisee of purchasing this option, the likelihood of franchisor-franchisee encroachment-related conflict is reduced. We also discuss structural results and explain our results using a numerical example. Journal of the Operational Research Society (2012) 63, 151-159. doi: 10.1057/jors.2010.184 Published online 8 June 2011

关键词： franchising territorial encroachment exclusivity stochastic dynamic programming

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Development of a stochastic multistage lifecycle programming model for electric power system planning - A case study for the Province of Saskatchewan, Canada

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2022年第0期158卷 112044-112044页

作者： Zhang, Xiaoyue Huang, Guohe Liu, Lirong Li, Kailong Univ Regina Environm Syst Engn Program Regina SK S4S 0A2 Canada Univ Surrey Ctr Environm & Sustainabil Guildford GU2 7XH Surrey England

In this study, a stochastic multistage lifecycle programming model (SMLP) for supporting the management of power systems and the associated economic and environmental risks is proposed. A two-fold objective is pursued. First, information on lifecycle GHG emissions from 10 forms of power generation technologies is comprehensively reviewed and characterized. Second, optimized pathways for the electricity system transition with specific consideration of lifecycle GHG emissions and lifecycle costs are identified. This work presents methodological advances in integrating the lifecycle concept with a power system optimization model, which can enhance the robustness of the resulting decision support. A case study for the Province of Saskatchewan is undertaken, where various uncertainties and risks are quantified and trade-offs among a number of system objectives/criteria are analyzed. According to the review, the lowest average emission per unit power generation is hydropower (12.8 g CO2-eq/kWh), closely followed by offshore wind power (14.6 g CO2-eq/kWh) and on-shore wind power (15.3 g CO2-eq/kWh). According to the modeling results, on-shore wind power is likely to become the dominant form of power generation in Saskatchewan by the end of the planning horizon;import power would play a big part in securing the province's electricity supply in the future. It is expected that the modeling results can help support the formulation of regional energy and relevant socio-economic and environmental policies.

关键词： Lifecycle assessment Lifecycle cost stochastic dynamic programming System optimization Power system planning

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