Conservativeness and monotonicity for learning algorithms

In the framework of PAC-learning model, relationships between learning processes and information compressing processes are investigated. Information compressing processes are formulated as weak Occam algorithms. A weak Occam algorithm is a deterministic polynomial time algorithm that, when given m examples of unknown function, outputs, with high probability, a representation of a function that is consistent with the examples and belongs to a function class with complexity o(m). It has been shown that a weak Occam algorithm is also a consistent PAC-learning algorithm. In this extended abstract, it is shown that the converse does not hold by giving a PAC-learning algorithm that is not a weak Occam algorithm, and also some natural properties, called conservativeness and monotonicity, for learning algorithms that might help the converse hold are given. In particular, the conditions that make a conservative PAC-learning algorithm a weak Occam algorithm are given, and it is shown that, under some natural conditions, a monotone PAC-learning algorithm for a hypothesis class can be transformed to a weak Occam algorithm without changing the hypothesis class.