EAGER: Event-Driven, Goal-Oriented Dynamic Resource Deployment

这一早期探索性研究奖章为动态资源分配优化问题的新理论和新方法的发展提供了支持。其目标是为这些问题提供一个增强但易于处理的框架，将现有方法的适用性扩大到更广泛、更现实的应用。这项研究在理论领域(开辟了新的研究路线)和跨不同领域的应用中具有变革的潜力，例如国防(例如，面向目标的异质资产部署，将故障成本降至最低)、医学(具有故障和累积成本的临床试验)、教育、健康监测和计算机科学(多模式传感器网络的动态运行)。动态资源分配问题传统上是在多臂强盗框架内处理的，受以下限制。在时间范围内的每个时间段，控制器激活独立项目的有限集合中的一个项目，在其他项目保持冻结的情况下推进所选项目的状态。从每个激活的项目中收集的奖励按固定比率贴现，要么对风险进行建模，要么计入复利。这些项目在时间尺度上是一致的，结构上也是对称的。本研究项目的主要目标是：i)打破统一的时间尺度限制。2)打破项目之间的结构对称性。为了实现这些目标，我们计划调查依赖于项目的“停顿事件”。这些停顿的事件允许对以不同速度运行的项目进行建模，并“挑出”项目--从成功的项目中获得回报，而在不成功的项目中招致成本。一个主要挑战是以一种能够洞察最优解决方案结构的方式对扩展框架进行建模。第二个挑战是为这些固有的大规模数据和优化问题开发有效的计算方法。

This EArly-Grant for Exploratory Research (EAGER) award provides support for the development of new theory and methods for optimization of dynamic resource allocation problems. Its objective is to provide an enhanced but tractable framework for these problems, expanding the applicability of existing methodology to broader, more realistic applications. This research has the potential to be transformative in the theoretical field (opening up new lines of research ) and in applications across diverse domains, such as defense (e.g., goal-oriented deployment of heterogeneous assets, minimizing cost of failure), medicine (clinical trials with failures and cumulative costs), education, health monitoring, and computer science (dynamic operation of multi-modal sensor networks).Dynamic resource allocation problems have been traditionally approached within the multi armed bandit framework, under the following restrictions. At each period over a time horizon, a controller activates one project of a finite collection of independent projects, advancing the state of the selected project while the others remain frozen. Rewards, collected from each activated project, are discounted at a constant rate, either modeling risk or accounting for compounding interest. There is a uniformity of the time-scale as well as a structural symmetry among the projects. The primary objectives of this research project are: i) To break the uniform time-scale restriction. ii) To break the structural symmetry among the projects. To achieve these goals we plan to investigate project dependent "halting events." These halting events allow the modeling of projects that operate at different rates, as well as "singling out" projects - generating rewards from successful projects and incurring costs for unsuccessful ones. A main challenge is to model the expanded frameworks in a way that makes it possible to obtain insight into the structure of optimal solutions. A second challenge is to develop efficient computational methods for these inherently large scale data and optimization problems.