The areas of On-Line Algorithms and Machine Learning are both concerned with problems of making decisions about the present based only on knowledge of the past. Although these areas differ in terms of their emphasis and the problems typically studied, there are a collection of results in Computational Learning Theory that fit nicely into the "on-line algorithms" framework. This survey article discusses some of the results, models, and open problems from Computational Learning Theory that seem particularly interesting from the point of view of on-line algorithms. The emphasis in this article is on describing some of the simpler, more intuitive results, whose proofs can be given in their entirity. Pointers to the literature are given for more sophisticated versions of these algorithms.

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We introduce a learning framework that combines elements of the well-known PAC and mistake-bound models. The KWIK (knows what it knows) framework was designed particularly for its utility in learning settings where active exploration can impact the training examples the learner is exposed to, as is true in reinforcement-learning and active-learning problems. We catalog several KWIK-learnable classes and open problems. 1.

Goldman and Kearns [GK91] recently introduced a notionof the teaching dimensionof a concept class. The teaching dimension is intended to capture the combinatorial difficulty of teaching a concept class. We present a computational analog which allows us to make statements about bounded-complexity teachers and learners, and we extend the model by incorporating trusted information. Under this extended model, we modify algorithms for learning several expressive classes in the exact identification model of Angluin [Ang88]. We study the relationships between variants of these models, and also touch on a relationship with distribution-free learning. 1 INTRODUCTION In the eight years since Valiant's seminal paper on learnability was published [Val84], computational learning theory has been an active and productive field. Several different learning models have been proposed, each attempting to model a different aspect of learning. Many of these models envision a teacher who interacts in some w...

One view of computational learning theory is that of a learner acquiring the knowledge of a teacher. We introduce a formal model of learning capturing the idea that teachers may have gaps in their knowledge. In particular, we consider learning from a teacher who labels examples "+" (a positive instance of the concept being learned), "\Gamma" (a negative instance of the concept being learned), and "?" (an instance with unknown classification), in such a way that knowledge of the concept class and all the positive and negative examples is not sufficient to determine the labelling of any of the examples labelled with "?". The goal of the learner is not to compensate for the ignorance of the teacher by attempting to infer "+" or "\Gamma" labels for the examples labelled with "?", but is rather to learn (an approximation to) the ternary labelling presented by the teacher. Thus, the goal of the learner is still to acquire the knowledge of the teacher, but now the learner must also ...

One characteristic of intelligence is adaptation. Computers should adapt to who is using them, how, why, when and where. The computer's representation of the user is called a user model; user modeling is concerned with developing techniques for representing the user and acting upon this information. The Doppelg anger system consists of a set of techniques for gathering, maintaining, and acting upon information about individuals, and illustrates my approach to user modeling. Work on Doppelg anger has been heavily influenced by the field of machine learning. This thesis has a twofold purpose: first, to set forth guidelines for the integration of machine learning techniques into user modeling, and second, to identify particular user modeling tasks for which machine learning is useful.

We investigate the complexity of learning for the well-studied model in which the learning algorithm may ask membership and equivalence queries. While complexity theoretic techniques have previously been used to prove hardness results in various learning models, these techniques typically are not strong enough to use when a learning algorithm may make membership queries. We develop a general technique for proving hardness results for learning with membership and equivalence queries (and for more general query models). We apply the technique to show that, assuming NP 6= co-NP, no polynomial-time membership and (proper) equivalence query algorithms exist for exactly learning read-thrice DNF formulas, unions of k 3 halfspaces over the Boolean domain, or some other related classes. Our hardness results are representation dependent, and do not preclude the existence of representation independent algorithms.

We explore the power of teaching by studying

. We present an off-line variant of the mistake-bound model of learning. Just like in the well studied on-line model, a learner in the offline model has to learn an unknown concept from a sequence of elements of the instance space on which he makes "guess and test" trials. In both models, the aim of the learner is to make as few mistakes as possible. The difference between the models is that, while in the on-line model only the set of possible elements is known, in the off-line model the sequence of elements (i.e., the identity of the elements as well as the order in which they are to be presented) is known to the learner in advance. We give a combinatorial characterization of the number of mistakes in the off-line model. We apply this characterization to solve several natural questions that arise for the new model. First, we compare the mistake bounds of an off-line learner to those of a learner learning the same concept classes in the on-line scenario. We show that the number of mis...

The exploration-exploitation tradeoff is crucial to reinforcement-learning (RL) agents, and a significant number of sample complexity results have been derived for agents in propositional domains. These results guarantee, with high probability, near-optimal behavior in all but a polynomial number of timesteps in the agent’s lifetime. In this work, we prove similar results for certain relational representations, primarily a class we call “relational action schemas”. These generalized models allow us to specify state transitions in a compact form, for instance describing the effect of picking up a generic block instead of picking up 10 different specific blocks. We present theoretical results on crucial subproblems in action-schema learning using the KWIK framework, which allows us to characterize the sample efficiency of an agent learning these models in a reinforcement-learning setting. These results are extended in an apprenticeship learning paradigm where and agent has access not only to its environment, but also to a teacher that can demonstrate traces of state/action/state sequences. We show that the class of action schemas that are efficiently learnable in this paradigm is strictly larger than those learnable in the online setting. We link