A novel strategy for solving the stochastic point location problem using a hierarchical searching scheme

Stochastic point location (SPL) deals with the problem of a learning mechanism (LM) determining the optimal point on the line when the only input it receives are stochastic signals about the direction in which it should move. One can differentiate the SPL from the traditional class of optimization problems by the fact that the former considers the case where the directional information, for example, as inferred from an Oracle (which possibly computes the derivatives), suffices to achieve the optimization-without actually explicitly computing any derivatives. The SPL can be described in terms of a LM (algorithm) attempting to locate a point on a line. The LM interacts with a random environment which essentially informs it, possibly erroneously, if the unknown parameter is on the left or the right of a given point. Given a current estimate of the optimal solution, all the reported solutions to this problem effectively move along the line to yield updated estimates which are in the neighborhood of the current solution.1 This paper proposes a dramatically distinct strategy, namely, that of partitioning the line in a hierarchical