Matrix computational analysis of probabilistic control systems

概率控制系统的矩阵计算分析

• 批准号: 371984-2010
• 负责人: Lu, Fletcher
• 金额: $ 1.09万
• 依托单位: University of Ontario Institute of Technology
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=572852
• 关键词: Matrix; computational; analysis; probabilistic; control

Probability matrices are produced from various applications where the environment can be represented by a network of conditional probability states. One such application is derived from machine learning robots that represent the world as a network of states following a Markov process, which retains no past state memory. Solving such classes of problems with a probability matrix component efficiently using scientific compuation theory is the main objective of this research program. Such classes of problems have solution methods that attempt to avoid the explicit solving of the resulting large system of equations as it is considered slow with worst case cubic runtime in the number of states and requiring a great deal of memory to store the system of equations. For instance, in the machine learning approach, a linear update approach is often used that is biased, but considered fast for its linear learning time and using only linear storage in the number of states in the environment. Numerical computation methods have made significant in-roads for efficiently solving matrix system problems, this research program will explore applying such techniques to this class of probability matrix problems to achieve the long-term objective of competitive computation time solutions (compared, for instance, to the often used biased linear machine learning approach) with minimal storage. The significant advantage of this approach is that it avoids problems such as the errors in a biased linear update method with a goal of producing competitively fast, accurate solutions.

概率矩阵是从各种应用中产生的，其中环境可以由条件概率状态的网络表示。 一个这样的应用程序来自机器学习机器人，它将世界表示为遵循马尔可夫过程的状态网络，该过程不保留过去的状态记忆。 使用科学计算理论有效地解决此类具有概率矩阵分量的问题是该研究计划的主要目标。 这类问题的求解方法试图避免显式求解所得到的大型方程组，因为它被认为是慢的，最坏情况下立方运行时间的状态数，并需要大量的存储器来存储方程组。 例如，在机器学习方法中，经常使用有偏差的线性更新方法，但由于其线性学习时间而被认为是快速的，并且仅使用环境中状态数量的线性存储。 数值计算方法在有效解决矩阵系统问题方面取得了重大进展，本研究计划将探索将此类技术应用于这类概率矩阵问题，以实现具有竞争力的计算时间解决方案的长期目标（例如，与经常使用的有偏线性机器学习方法相比）。这种方法的显著优点是，它避免了诸如有偏线性更新方法中的误差之类的问题，其目标是产生具有竞争力的快速、准确的解决方案。