Characterization of the absolutely expedient learning algorithms for stochastic automata in a non-discrete space of actions

摘要

This work presents a learning algorithm to reach the optimum action of an arbitrary set of actions contained in R~m. An initial and arbitrary probability' measure on R~m allow us to select an action and the probability is sequentially updated by a stochastic automaton using the response of the environment to the selected action. We prove that the corresponding random sequence of probability measures converges in law to a probability measure degenerate on the optimum action, with probability as close to one as we desire.