Steps or Stages for Incremental Learning

Dominique Luzeaux and Eric Martin

Formal work on learning consists in an ever growing class of paradigms, which may be strongly related or may only share very few points. Our research is concerned with the following issue: how to learn to control a physical system. This is a major field of interest for AI, and many proposals have emerged to solve this problem. But the most part of it is mainly empirical work and is not concerned with the theoretical work we mentioned above. In this paper we would like to describe a few methodological principles that are valuable with respect to two issues: on the one hand we can find techniques that implement them and we can eventually write programs that learn to control a system; on the other hand we can study paradigms that take those principles as axioms. Such paradigms are very different from the usual ones and give a new insight on incremental learning. In the first section we will present in a rather informal way the methodological principles we had to introduce in order to tackle our learning problem. We will show how they differ from usual principles and why their introduction was necessary. A close investigation of the relationship between the flow of data and the hypotheses proposed by the learner will lead to the notion of learning stages rather than learning steps. In the same way as we had to adapt learning methodologies to deal with a control problem, we had to find within control theory a framework within which learning was possible. This will be discussed in the second section. In the third section, we will give one possible formalization of the methodological principles of the first section, in order to formulate a result which shows precisely why the concept of stage is an important one.

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