On How to Learn from a Stochastic Teacher or a Stochastic Compulsive Liar of Unknown Identity

Abstract

We consider the problem of a learning mechanism (robot, or algorithm) that learns a parameter while interacting with either a stochastic teacher or a stochastic compulsive liar. The problem is modeled as follows: the learning mechanism is trying to locate an unknown point on a real interval by interacting with a stochastic environment through a series of guesses. For each guess the environment (teacher) essentially informs the mechanism, possibly erroneously, which way it should move to reach the point. Thus, there is a non-zero probability that the feedback from the environment is erroneous. When the probability of correct response is p>0.5, the environment is said to be Informative, and we have the case of learning from a stochastic teacher. When this probability is p<0.5 the environment is deemed Deceptive, and is called a stochastic compulsive liar.

This paper describes a novel learning strategy by which the unknown parameter can be learned in both environments. To the best of our knowledge, our results are the first reported results which are applicable to the latter scenario. Another main contribution of this paper is that the proposed scheme is shown to operate equally well even when the learning mechanism is unaware whether the environment is Informative or Deceptive. The learning strategy proposed herein, called CPL–ATS, partitions the search interval into three equi-sized sub-intervals, evaluates the location of the unknown point with respect to these sub-intervals using fast-converging ε-optimal L _RI learning automata, and prunes the search space in each iteration by eliminating at least one partition. The CPL-ATS algorithm is shown to be provably converging to the unknown point to an arbitrary degree of accuracy with probability as close to unity as desired. Comprehensive experimental results confirm the fast and accurate convergence of the search for a wide range of values for the environment’s feedback accuracy parameter p. The above algorithm can be used to learn parameters for non-linear optimization techniques.