Structural measures for games and process control in the branch learning model

Abstract

Process control problems can be modeled as closed recursive games. Learning strategies for such games is equivalent to the concept of learning infinite recursive branches for recursive trees. We use this branch learning model to measure the difficulty of learning and synthesizing process controllers. We also measure the difference between several process learning criteria, and their difference to controller synthesis. As measure we use the information content (i.e., the Turing degree) of the oracle which a machine needs to get the desired power. The investigated learning criteria are finite, EX-, BC-, weak BC- and on-line learning. Finite, EX- and BC-style learning are well known from inductive inference, while weak BC- and on-line learning came up with the new notion of branch (i.e., process) learning. For all considered criteria – including synthesis – we also solve the questions of their trivial degrees, their omniscient degrees and with some restrictions their inference degrees. While most of the results about finite, EX- and BC-style branch learning can be derived from inductive inference, new techniques had to be developed for on-line learning, weak BC-style learning and synthesis, and for the comparisons of all process learning criteria with the power of controller synthesis.