Operant conditioning is one of the fundamental mechanisms of animal learning, which suggests that the behavior of all animals, from protists to humans, is guided by its consequences. We present a new stochastic learning automaton called a Skinner au- tomaton that is a psychological model for formalizing the theory of operant conditioning. We identify animal operant learning with a thermodynamic process, and derive a so-called Skinner algorithm from Monte Carlo method as well as Metropolis algo- rithm and simulated annealing. Under certain conditions, we prove that the Skinner automaton is expedient, 6-optimal, optimal, and that the operant probabilities converge to the set of stable roots with probability of 1. The Skinner automaton enables ma- chines to autonomously learn in an animal-like way.
