Foreword 
Algorithmic learning theory is mathematics about computer
programs which learn from experience. This involves considerable interaction
between various mathematical disciplines including
theory of computation, statistics, and combinatorics.
There is also considerable interaction
with the practical, empirical fields of machine and statistical
learning in which a principal aim is to predict, from past data about
phenomena, useful features of future data from the same phenomena.
The papers in this volume cover a broad range of topics of current research in the field of algorithmic learning theory. We have divided the 29 technical, contributed papers in this volume into eight categories (corresponding to eight sessions) reflecting this broad range. The categories featured are Inductive Inference, Approximate Optimization Algorithms, Online Sequence Prediction, Statistical Analysis of Unlabeled Data, PAC Learning & Boosting, Statistical Supervised Learning, Logic Based Learning, and Query & Reinforcement Learning. Below we give a brief overview of the field, placing each of these topics in the general context of the field. Formal models of automated learning reflect various facets of the wide range of activities that can be viewed as learning. A first dichotomy is between viewing learning as an indefinite process and viewing it as a finite activity with a defined termination. Inductive Inference models focus on indefinite learning processes, requiring only eventual success of the learner to converge to a satisfactory conclusion. When one wishes to predict future data, success can be enhanced by making some restrictive but true assumptions about the nature (or regularities) of the data stream. In the learning theory community, this problem is addressed in two different ways. The first is by assuming that the data to be predicted is generated by an operator that belongs to a restricted set of operators that is known to the learner a priori. The PAC model and some of the work under the Inductive Inference framework follow this path. Alternatively, one could manage without any such prior assumptions by relaxing the success requirements of the learner: rather than opting for some absolute degree of accuracy, the learner is only required to perform as well as any learner in some fixed family of learners. Thus, if the data is erratic or otherwise hard to predict, the learner can ignore poor accuracy as long as no member of the fixed reference family of learners can do no better. This is the approach taken by some Online Sequence Prediction models in the indefinite learning setting and, also, by most of the models of Statistical Learning in the finite horizon framework. Boosting is a general technique that applies a given type of learner iteratively to improve its performance. Boosting approaches have been shown to be effective for a wide range of learning algorithms and have been implemented by a variety of methods. A second dichotomy is between Supervised and UnSupervised learning. The latter we refer to as learning from Unlabeled Data. In the first scenario, the data has the form of an examplelabel pairs. The learner is trained on a set of such pairs and then, upon seeing some fresh examples, has to predict their labels. In the latter model, the data points lack any such labeling, and the learner has to find some persistent regularities in the data, on the basis of the examples it has seen. Such regularities often take the form of partitioning the data into clusters of similar points, but in some cases take other forms, such as locating the boundaries of the support of the data generating distribution. Many learning algorithms can be viewed as searching for an object that fits the given training data best. Such optimization tasks are often computationally infeasible. To overcome such computational hurdles, it is useful to apply algorithms that search for approximations to the optimal objects. The study of such algorithms, in the context of learning tasks, is the subject of our Approximate Optimization Algorithms session. There is a large body of research that examines different representations of data and of learners' conclusions. This research direction is the focus of our Logic Based Learning session. A final important dichotomy separates models of interactive learning from those that model passive learners. In the first type of learning scenarios the actions of the learner affect the training data available to it. In the Query Learning model this interaction takes the form of queries of certain (preindicated) type(s) that the learner can pose. Then the data upon which the learner bases its conclusions are the responses to these queries. The other model that addresses interactive learning is Reinforcement Learning, a model that assumes that the learner takes actions and receives rewards that are a function of these actions. These rewards in turn are used by the learner to determine its future actions.
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