AI 2003: Advances in Artificial Intelligence

Consider the problem of a robot (algorithm, learning mechanism) moving along the real line attempting to locate a particular point ? . To assist the me- anism, we assume that it can communicate with an Environment ("e;Oracle"e;) which guides it with information regarding the direction in which it should go. If the Environment is deterministic the problem is the "e;Deterministic Point - cation Problem"e; which has been studied rather thoroughly [1]. In its pioneering version [1] the problem was presented in the setting that the Environment could charge the robot a cost which was proportional to the distance it was from the point sought for. The question of having multiple communicating robots locate a point on the line has also been studied [1, 2]. In the stochastic version of this problem, we consider the scenario when the learning mechanism attempts to locate a point in an interval with stochastic (i. e. , possibly erroneous) instead of deterministic responses from the environment. Thus when it should really be moving to the "e;right"e; it may be advised to move to the "e;left"e; and vice versa. Apart from the problem being of importance in its own right, the stoch- tic pointlocationproblemalsohas potentialapplications insolvingoptimization problems. Inmanyoptimizationsolutions-forexampleinimageprocessing,p- tern recognition and neural computing [5, 9, 11, 12, 14, 16, 19], the algorithm worksits wayfromits currentsolutionto the optimalsolutionbasedoninfor- tion that it currentlyhas. A crucialquestionis oneof determining the parameter whichtheoptimizationalgorithmshoulduse.