CDS&E-MSS/Collaborative Research: Sequential Design for Stochastic Control: Active Learning of Optimal Policies

CDS

• 批准号: 1521702
• 负责人: Robert Gramacy
• 金额: $ 22.85万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2018-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1521702&HistoricalAwards=false
• 关键词: CDS& MSS; Collaborative; Research; Sequential

This research project aims to build new cross-disciplinary algorithms that blend concepts from applied probability, control, and statistical modeling to tackle computational challenges in large-scale optimization. Creation of such new links is another step in building a next-generation of high-performance algorithms needed to meet the increasingly complex problems arising in applications as diverse as finance, energy storage and security, and the management of epidemics. The project's research agenda is grounded in two concrete application areas where it is crucial to tackle industrial-grade high-fidelity models. One is the efficient management of cycled commodity assets, including gas storage, battery storage, or fleets of power plants as energy infrastructure is transitioned to the "smart grid." A second is timely and effective response to unfolding infectious disease outbreaks, notably influenza. Both present major cross-disciplinary challenges. We see vast potential for algorithms which expand capabilities for aspects of quantitative control, and thus provide higher quality information to decision makers. Our goal is to produce a smarter, more targeted, use of random numbers in a new wave of lean stochastic solvers, and subsequently an expansion of the size of problems that can be tackled with existing computing capabilities. The educational core of the project contributes to inter-disciplinary training in mathematical sciences across undergraduate, graduate and postdoctoral levels. The collaborative initiatives will also enhance the research infrastructure through exchange of ideas between the two campuses (Univesrity of California-Santa Barbara and University of Chicago) and communities of statisticians, operations researchers and engineers. All algorithms would be documented and publicly released to the wider scientific community. Deployment of simulation based schemes remains key for control of stochastic systems that require realistic high-fidelity representations. This project will develop new Monte Carlo algorithms for a class of stochastic control problems by erecting novel bridges between dynamic control and methods of sequential design and statistical learning. Our research agenda hinges on sequential, active learning of optimal action sets, so that the algorithms adaptively allocate computing resources to better enhance fidelity of the approximated control strategies. Such targeted use of Monte Carlo simulations links approximate dynamic programming with response surface modeling, marrying two so-far disparate areas of applied mathematics and statistics. The resulting adaptive schemes will facilitate orders of magnitude savings in simulation budgets, expanding the frontier for predictive modeling and decision making under uncertainty. The proposed research will advance the theory of algorithms for dynamic control over massive multi-dimensional state spaces, where curses of dimensionality are unavoidable. Simultaneously, integration of the statistical and computational theories in this direction will open new lines of interdisciplinary quantitative research. Through enhancing knowledge discovery in large-scale control settings, the projects will facilitate transition to practice in novel contexts. With the aim of reaching out to diverse users from the mathematical, biological, physical and engineering sciences, producing general purpose open-source software via R packages is a primary deliverable of the project, and will be supplemented by a database of case studies.

该研究项目旨在构建新的跨学科算法，这些算法将应用概率，控制和统计建模融合在一起，以应对大规模优化的计算挑战。建立这种新链接是建立下一代高性能算法的又一步，以满足诸如金融，储能和安全等多样化的应用程序中越来越复杂的问题以及流行病的管理。该项目的研究议程基于两个具体的应用领域，在该领域对于解决工业级高保真模型至关重要。一个是对循环商品资产的有效管理，包括存储，电池存储或发电厂的机队，因为能源基础设施已过渡到“智能电网”。第二次是及时有效的反应，对开发感染性疾病暴发，尤其是流感。两者都面临着重大的跨学科挑战。我们看到算法的巨大潜力，这些算法扩大了定量控制方面的能力，从而为决策者提供了更高质量的信息。我们的目标是在新的精益随机求解器中生产更智能，更有针对性的，随机数的使用，然后扩大了可以通过现有计算能力来解决的问题大小的扩展。该项目的教育核心有助于跨本科，研究生和博士后水平的数学科学跨学科培训。该协作计划还将通过在两个校园（加利福尼亚 - 圣塔芭芭拉大学和芝加哥大学的Univerile）之间以及统计学家，运营研究人员和工程师社区之间交换思想，从而增强研究基础设施。所有算法都将记录并公开发给更广泛的科学界。基于模拟的方案的部署仍然是控制需要现实的高保真表示形式的随机系统的关键。该项目将通过在动态控制和顺序设计和统计学习方法之间建立新的桥梁来开发新的蒙特卡洛算法，以针对一类随机控制问题。我们的研究议程取决于对最佳动作集的顺序积极学习，因此算法会自适应地分配计算资源，以更好地提高近似控制策略的保真度。这种有针对性的使用蒙特卡洛模拟将近似动态编程与响应表面建模联系起来，与应用数学和统计数据的两个SO-FAR不同领域结合在一起。由此产生的自适应方案将有助于在模拟预算中节省数量级，从而扩大了不确定性下预测性建模和决策的前沿。拟议的研究将推进对大规模多维状态空间的动态控制算法理论，其中不可避免地会有维数的诅咒。同时，统计和计算理论在这个方向上的整合将开放跨学科定量研究的新线条。通过增强大规模控制设置中的知识发现，这些项目将有助于在新颖背景下过渡到实践。为了与数学，生物学，物理和工程科学接触不同的用户，通过R软件包生产通用开源软件是该项目的主要可交付方式，并将通过案例研究数据库来补充。