This paper reports on experiments where techniques of supervised machine learning are applied to the problem of planning. The input to the learning algorithm is composed of a description of a planning domain, planning problems in this domain, and solutions for them. The output is an efficient algorithm --- a strategy --- for solving problems in that domain. We test the strategy on an independent set of planning problems from the same domain, so that success is measured by its ability to solve complete problems. A system, L2Act, has been developed in order to perform these experiments. We have experimented with the blocks world domain, and the logistics domain, using strategies in the form of a generalization of decision lists, where the rules on the list are existentially quantified first order expressions. The learning algorithm is a variant of Rivest`s [39] algorithm, improved with several techniques that reduce its time complexity. As the experiments demonstrate, generalization is a...

Abstract. We introduce a new framework for the study of reasoning. The Learning (in order) to Reason approach developed here views learning as an integral part of the inference process, and suggests that learning and reasoning should be studied together. The Learning to Reason framework combines the interfaces to the world used by known learning models with the reasoning task and a performance criterion suitable for it. In this framework, the intelligent agent is given access to its favorite learning interface, and is also given a grace period in which it can interact with this interface and construct a representation KB of the world W. The reasoning performance is measured only after this period, when the agent is presented with queries � from some query language, relevant to the world, and has to answer whether W implies �. The approach is meant to overcome the main computational difficulties in the traditional treatment of reasoning which stem from its separation from the “world”. Since the agent interacts with the world when constructing its knowledge representation it can choose a representation that is useful for the task at hand. Moreover, we can now make explicit the dependence of the reasoning performance on the environment the agent interacts with. We show how previous results from learning theory and reasoning fit into this framework and

We formalize a model for supervised learning of action strategies in dynamic stochastic domains and show that PAC-learning results on Occam algorithms hold in this model as well. We then identify a class of rule-based action strategies for which polynomial time learning is possible. The representation of strategies is a generalization of decision lists; strategies include rules with existentially quantified conditions, simple recursive predicates, and small internal state, but are syntactically restricted. We also study the learnability of hierarchically composed strategies where a subroutine already acquired can be used as a basic action in a higher level strategy. We prove some positive results in this setting, but also show that in some cases the hierarchical learning problem is computationally hard. 1 Introduction We formalize a model for supervised learning of action strategies in dynamic stochastic domains, and study the learnability of strategies represented by rule-based syste...

We investigate the problem of learning DNF concepts from examples using decision trees as a concept description language. Due to the replication problem, DNF concepts do not always have a concise decision tree description when the tests at the nodes are limited to the initial attributes. However, the representational complexity may be overcome by using high level attributes as tests. We present a novel algorithm that modifies the initial bias determined by the primitive attributes by adaptively enlarging the attribute set with high level attributes. We show empirically that this algorithm outperforms a standard decision tree algorithm for learning small random DNF with and without noise, when the examples are drawn from the uniform distribution. 1

This paper surveys some recent theoretical results on the efficiency of machine learning algorithms. The main tool described is the notion of Probably Approximately Correct (PAC) learning, introduced by Valiant. We define this learning model and then look at some of the results obtained in it. We then consider some criticisms of the PAC model and the extensions proposed to address these criticisms. Finally, we look briefly at other models recently proposed in computational learning theory. 2 Introduction It's a dangerous thing to try to formalize an enterprise as complex and varied as machine learning so that it can be subjected to rigorous mathematical analysis. To be tractable, a formal model must be simple. Thus, inevitably, most people will feel that important aspects of the activity have been left out of the theory. Of course, they will be right. Therefore, it is not advisable to present a theory of machine learning as having reduced the entire field to its bare essentials. All ...

In this paper we study learning in the PAC model of Valiant [18] in which the example oracle used for learning may be faulty in one of two ways: either by misclassifying the example or by distorting the distribution of examples. We first consider models in which examples are misclassified. Kearns [12] recently showed that efficient learning in a new model using statistical queries is a sufficient condition for PAC learning with classification noise. We show that efficient learning with statistical queries is sufficient for learning in the PAC model with malicious error rate proportional to the required statistical query accuracy. One application of this result is a new lower bound for tolerable malicious error in learning monomials of k literals. This is the first such bound which is independent of the number of irrelevant attributes n. We also use the statistical query model to give sufficient conditions for using distribution specific algorithms on distributions outside their prescr...

We address well-studied problems concerning the learnability of parities and halfspaces in the presence of classification noise. Learning of parities under the uniform distribution with random classification noise, also called the noisy parity problem is a famous open problem in computational learning. We reduce a number of basic problems regarding learning under the uniform distribution to learning of noisy parities. We show that under the uniform distribution, learning parities with adversarial classification noise reduces to learning parities with random classification noise. Together with the parity learning algorithm of Blum et al. [5], this gives the first nontrivial algorithm for learning parities with adversarial noise. We show that learning of DNF expressions reduces to learning noisy parities of just logarithmic number of variables. We show that learning of k-juntas reduces to learning noisy parities of k variables. These reductions work even in the presence of random classification noise in the original DNF or junta. We then consider the problem of learning halfspaces over Qn with adversarial noise or finding a halfspace that maximizes the agreement rate with a given set of examples. We prove an essentially optimal hardness factor of 2 − ɛ, improving the factor of 85 84 − ɛ due to Bshouty and Burroughs [8]. Finally, we show that majorities of halfspaces are hard to PAC-learn using any representation, based on the cryptographic assumption underlying the Ajtai-Dwork cryptosystem.

We exhibit efficient algorithms for agnostic PAC-learning with rectangles, unions of two rectangles, and unions of k intervals as hypotheses. These hypothesis classes are of some interest from the point of view of ap-plied machine learning, because empirical studies show that hypotheses of this simple type (in just one or two of the attributes) provide good prediction rules for various real-world classification problems. In addition, optimal hypotheses of this type may provide valuable heuristic insight into the structure of a real-world classification problem, The algorithms that are introduced in this paper make it feasible to compute optimal hypotheses of this type for a training set of several hundred examples. We also exhibit an approximation algorithm that can compute nearly optimal hypotheses for much larger datasets.

This paper studies the robustness of PAC learning algorithms when the instance space is f0; 1g n , and the examples are corrupted by purely random noise affecting only the attributes (and not the labels). For uniform attribute noise, in which each attribute is flipped independently at random with the same probability, we present an algorithm that PAC learns monomials for any (unknown) noise rate less than 1=2. Contrasting this positive result, we show that product random attribute noise, where each attribute i is flipped randomly and independently with its own probability p i , is nearly as harmful as malicious noise---no algorithm can tolerate more than a very small amount of such noise. Supported in part by a GE Foundation Junior Faculty Grant and NSF grant CCR-9110108. Part of this research was conducted while the author was at the M.I.T. Laboratory for Computer Science and supported by NSF grant DCR-8607494 and a grant from the Siemens Corporation. Net address: sg@cs.wustl.edu....

Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, including rectangles and halfspaces. In addition, we give extensions to other discrepancy problems. 1. Introduction The main theme of this paper is to present efficient algorithms that solve the problem of computing the maximum bichromatic discrepancy for axis oriented rectangles. This problem arises naturally in different areas of computer science, such as computational 1 The research work of these authors was supported by NSF Grant CCR93-01254 and the Geometry Center. learning theory, computational geometry and computer graphics ([Ma], [DG]), and has applications in all these areas. In computational learning theory, the problem of agnostic PAC-learning with simple geometric hypothese...