Matrix computational analysis of probabilistic control systems

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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.