Non-linear Optimization Methods for Learning Regular Distributions

Wenjing Chu, Shuo Chen, Marcello M. Bonsangue

Abstract: Probabilistic finite automata (PFA) are recognizers of regular distributions over finite strings, a model that is widely applied in speech recognition and biological systems, for example. While the underlying structure of a PFA is just that of a normal automaton, it is well known that PFA with a non-deterministic underlying structure is more powerful than deterministic one. In this paper, we concentrate on passive learning non-deterministic PFA from examples and counterexamples using a two steps procedure: first we learn the underlying structure using an algorithm for learning the underlying residual finite state automaton, then we learn the probabilities of states and transitions using three different optimization methods. We experimentally show with a set of random probabilistic finite automata that the ones learned using RFSA combined with genetic algorithm for optimizing the weight outperforms other existing methods greatly improving the distance to the automaton to be learned. We also apply our algorithm to model the behavior of an agent in a maze. Also here RFSA algorithms have better performance than existing automata learning methods and can model both positive and negative samples well.