AUTOMATA LEARNING AND INTELLIGENT TERTIARY SEARCHING FOR STOCHASTIC POINT LOCATION

Consider the problem of a robot (learning mechanism or algorithm) atte mpting to locate a point on a line. The mechanism interacts with a ran dom environment which essentially informs it, possibly erroneously, wh ich way it should move. The first reported paper to solve this problem [14] presented a solution which operated in a discretized space. In t his paper we present a new scheme by which the point can be learnt usi ng a combination of various learning principles. The heart of the stra tegy involves performing a controlled random walk on the underlying sp ace and then intelligently pruning the space using an adaptive tertiar y search, The overall learning scheme is shown to be E-optimal. Just a s in the case of the results presented in [14] the application of the solution in nonlinear optimization has been alluded to. In a typical o ptimization process the algorithm has to work its way toward the maxim um (minimum) using local information. However, the crucial issue in th ese strategies is that of determining the parameter to be used in the optimization itself, If the parameter is too small the convergence is sluggish. On the other hand, if the parameter is too large, the system could erroneously converge or even oscillate. The strategy presented here can be utilized to determine the best parameter to be used in the optimization.