In this chapter we will deal with “mechanizing” induction, i.e. with ways in which theoretical computer science approaches inductive generalization. In the field of Machine Learning, algorithms for induction are developed. Depending on the form of the available data, the nature of these algorithms may be very different. Some of them combine geometric and statistical ideas, while others use classical reasoning based on logical formalism. However, we are not so much interested in the algorithms themselves, but more on the philosophical (...) and theoretical foundations they share. Thus in the first of two parts, we will examine different approaches and inductive assumptions in two particular learning settings. While many machine learning algorithms work well on a lot of tasks, the interpretation of the learned hypothesis is often difficult. Thus, while e.g. an algorithm surprisingly is able to determine the gender of the author of a given text with about 80 percent accuracy [Argamon and Shimoni, 2003], for a human it takes some extra effort to understand on the basis of which criteria the algorithm is able to do so. With that respect the advantage of approaches using logic are obvious: If the output hypothesis is a formula of predicate logic, it is easy to interpret. However, if decision trees or algorithms from the area of inductive logic programming are based purely on classical logic, they suffer from the fact that most universal statements do not hold for exceptional cases, and classical logic does not offer any convenient way of representing statements which are meant to hold in the “normal case”. Thus, in the second part we will focus on approaches for Nonmonotonic Reasoning that try to handle this problem. Both Machine Learning and Nonmonotonic Reasoning have been anticipated partially by work in philosophy of science and philosophical logic. At the same time, recent developments in theoretical computer science are expected to trig- ger further progress in philosophical theories of inference, confirmation, theory revision, learning, and the semantic and pragmatics of conditionals. We hope this survey will contribute to this kind of progress by building bridges between computational, logical, and philosophical accounts of induction. (shrink)

Work in online learning traditionally considered induction-friendly (e.g. stochastic with a fixed distribution) and induction-hostile (adversarial) settings separately. While algorithms like Exp3 that have been developed for the adversarial setting are applicable to the stochastic setting as well, the guarantees that can be obtained are usually worse than those that are available for algorithms that are specifically designed for stochastic settings. Only recently, there is an increasing interest in algorithms that give (near-)optimal guarantees with respect to the underlying setting, even (...) in case its nature is unknown to the learner. In this paper, we review various online learning algorithms that are able to adapt to the hardness of the underlying problem setting. While our focus lies on the application of adaptive algorithms as meta-inductive methods that combine given base methods, concerning theoretical properties we are also interested in guarantees that go beyond a comparison to the best fixed base learner. (shrink)

We consider a reinforcement learning setting where the learner is given a set of possible models containing the true model. While there are algorithms that are able to successfully learn optimal behavior in this setting, they do so without trying to identify the underlying true model. Indeed, we show that there are cases in which the attempt to find the true model is doomed to failure.

We give an example from the theory of Markov decision processes which shows that the “optimism in the face of uncertainty” heuristics may fail to make any progress. This is due to the impossibility to falsify a belief that a (transition) probability is larger than 0. Our example shows the utility of Popper’s demand of falsifiability of hypotheses in the area of artificial intelligence.