A General Strategy for Solving the Stochastic Point Location Problem by Utilizing the Correlation of Three Adjacent Nodes

Abstract

Stochastic Point location (SPL) problem, in which a learning machine (LM) (entity, robot, algorithm, etc) tries to locate a certain point in an interval, belongs to the area of Machine Learning. During the process, LM is interactive with a stochastic environment so that the information available is probably wrong. In some conventional methods, the line is sampled into discrete points and the authors mainly consider the relation between two neighboring nodes. Thus there is plenty of space for improvement in performance. In this paper, we expand the relation from two neighboring nodes to three adjacent nodes based on the classical random walk-based triple level algorithm (RWTA), and subsequently propose a general algorithm. The philosophy lies in a newly-introduced parameter ?, which is defined as the radio of the correlation between adjacent nodes to the correlation between spaced nodes. It varies from zero to one, and particularly if ? = 1, the algorithm could be exactly evolved into RWTA. That is why the proposed algorithm is declared as a generalized version. For the reason that the whole strategy could be regarded as the Markov chain, its transform diagram and transform matrix are construed, followed by a rigorous mathematical proof procedure of the convergence. It can be computed that the proposed algorithm gets a larger stably convergent interval with p>0.236 if ? = 0, extending far beyond either Oommen's algorithm with p > 0.5 or RWTA with p > 0.333. The experimental results demonstrate the effectiveness and efficiency of the proposed algorithm. By comparing it with the exiting algorithms, the proposed one is superior to others not only in stability but also in speed.