Optimal Decision Strategies for Large Spatio-Temporal Decision Problems

当前的一些公共卫生、生态和环境危机可以被概念化为时空决策问题，其中有害的复制因子在空间中传播，同时，决策者必须选择何时、何地以及如何分配有限的资源，以控制该因子的传播。例如，一种传染病在社交网络中的人际传播，一种计算机病毒在网络中的机器之间传播，以及一种入侵物种在生态景观中的传播。这些流行病的代价是巨大的。例如，全球32%的死亡归因于传染病，计算机病毒给美国企业造成的损失估计每年超过600亿美元，入侵物种造成的损失估计每年超过1000亿美元，影响1亿英亩的土地。因此，改进时空决策可以给社会各部门带来巨大的利益。技术的进步使得收集、存储和操作大量数据变得越来越容易。该研究项目朝着使用积累复制代理传播数据的方法迈出了第一步，这些数据可以告知资源随时间的分配。该方法调整了非平稳代理动态，不断变化的资源可用性，以及不确定或不完整的测量。控制复制因子在空间和时间上的传播的一个关键组成部分是决定何时、何地以及如何应用干预措施。这种控制过程被形式化为一种分配策略，该策略由一系列函数组成，每个时间点一个函数，这些函数将智能体传播的最新信息映射到位置子集上的分布，以接收干预。该项目正式定义了一个使用潜在结果的最优分配策略，并证明空间接近会导致地点之间的因果干扰，从而阻止直接应用现有方法进行顺序处理分配。利用系统动力学模型和仿真优化，提出了一种在预先指定的分配策略类别中最优策略的参数估计方法。该估计器方差小，可以应用于数据贫乏的环境中，但如果系统动力学模型指定不当，则可能存在高偏差。本文还提出了一种不需要正确指定系统动力学模型的最优分配策略的半参数估计。由于半参数估计器对潜在系统动力学的假设较少，因此它对模型错误规范具有潜在的鲁棒性，但可能具有很高的方差。为了平衡偏差和方差，并优化有限样本性能，将研究半参数估计器对参数估计器的收缩。这些方法将通过应用于蝙蝠白鼻综合征的传播来说明。

A number of current public health, ecological, and environmental crises can be conceptualized as spatio-temporal decision problems wherein a harmful replicating agent is spreading across space and, simultaneously, a decision maker must select when, where, and how to allocate limited resources targeted at controlling the spread of the agent. Examples include the spread of an infectious disease across people in a social network, the spread of a computer virus across machines in a network, and the spread of an invasive species across an ecological landscape. The costs of these epidemics are enormous. For example, 32% of global deaths are attributed to infectious diseases, the cost of computer viruses to U.S. businesses is estimated to exceed 60 billion dollars per year, and the cost of invasive species is estimated to exceed 100 billion dollars per year and to affect 100 million acres of land. Thus, improvements to spatio-temporal decision making could have tremendous benefits to all sectors of society. Technological advances have made it increasingly easy to collect, store, and manipulate large amounts of data. This research project takes first steps toward methods that use accumulating data on the spread of a replicating agent to inform resource allocation over time. The methodology adjusts for non-stationary agent dynamics, changing availability of resources, and uncertain or incomplete measurements.A key component of controlling the spread of a replicating agent over space and time is deciding where, when, and how to apply interventions. This control process is formalized as an allocation strategy which comprises a sequence of functions, one per time point, that map up-to-date information on the spread of the agent to a distribution over subsets of locations to receive an intervention. The project formally defines an optimal allocation strategy using potential outcomes, and demonstrates that spatial proximity induces causal interference among locations, thereby preventing direct application of existing methods for sequential treatment assignment. A parametric estimator of the optimal strategy within a pre-specified class of allocation strategies using a systems dynamics model and simulation-optimization is developed. This estimator has low variance and can be applied in a data-impoverished setting, however it may suffer from high bias if the systems dynamics model is misspecified. A semi-parametric estimator of the optimal allocation strategy which does not require correct specification of a systems dynamics model is also developed. Because the semi-parametric estimator relies on fewer assumptions about the underlying systems dynamics, it is potentially robust to model misspecification but may have high variance. To balance bias and variance, and optimize finite sample performance, shrinkage of the semi-parametric estimator toward the parametric estimator will be investigated. The methodologies will be illustrated with an application to the spread of white-nose syndrome in bats.