Parameter learning from stochastic teachers and stochastic compulsive liars

This paper considers a general learning problem akin to the field of learning automata (LA) in which the learning mechanism attempts to learn from a stochastic teacher or a stochastic compulsive liar. More specifically, unlike the traditional LA model in which LA attempts to learn the optimal action offered by the Environment (also here called the "Oracle"), this paper considers the problem of the learning mechanism (robot, an LA, or in general, an algorithm) attempting to learn a "parameter" within a closed interval. 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 informed guesses. For each guess, the Environment essentially informs the mechanism, possibly erroneously (i.e., with probability p), which way it should move to reach the unknown point. When the probability of a correct response is p > 0.5, the Environment is said to be informative, and thus the case of learning from a stochastic teacher. When this probability 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. These results are the first reported results, which are applicable to the latter scenario. The most significant contribution of this paper is that the proposed scheme is shown to operate equally well, even when the learning mechanism is unaware of whether the Environment ("Oracle") is informative or deceptive. The learning strategy proposed herein, called CPL-AdS, partitions the search interval into d subintervals, evaluates the location of the unknown point with respect to these subintervals using fast-converging E-optimal LRI LA, and prunes the search space in each iteration by eliminating at least one partition. The CPL-AdS algorithm is shown to provably converge to the unknown point with 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, and thus has numerous potential applications.