Marcus Hutter

Universal Intelligence: A Definition of Machine Intelligence

A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: we take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.

A New Local Distance-Based Outlier Detection Approach for Scattered Real-World Data

Detecting outliers which are grossly different from or inconsistent with the remaining dataset is a major challenge in real-world KDD applications. Existing outlier detection methods are ineffective on scattered real-world datasets due to implicit data patterns and parameter setting issues. We define a novel Local Distance-based Outlier Factor (LDOF) to measure the outlier-ness of objects in scattered datasets which addresses these issues. LDOF uses the relative location of an object to its neighbours to determine the degree to which the object deviates from its neighbourhood. We present theoretical bounds on LDOFs false-detection probability. Experimentally, LDOF compares favorably to classical KNN and LOF based outlier detection. In particular it is less sensitive to parameter values.

A Monte-Carlo AIXI approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. Our approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a new Monte-Carlo Tree Search algorithm along with an agent-specific extension to the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a variety of stochastic and partially observable domains. We conclude by proposing a number of directions for future research.

UNIVERSAL ALGORITHMIC INTELLIGENCE A mathematical top!down approach

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff’s theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is un-computable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t·2l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.

Fitness uniform selection to preserve genetic diversity

In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of more fit individuals. The right selection pressure is critical in ensuring sufficient optimization progress on the one hand and in preserving genetic diversity to be able to escape from local optima on the other. We propose a new selection scheme, which is uniform in the fitness values. It generates selection pressure towards sparsely populated fitness regions, not necessarily towards higher fitness, as is the case for all other selection schemes. We show that the new selection scheme can be more effective than standard selection schemes.

A Philosophical Treatise of Universal Induction

Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches.

Fitness uniform optimization

In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of fitter individuals. The right selection pressure is critical in ensuring sufficient optimization progress on the one hand and in preserving genetic diversity to be able to escape from local optima on the other hand. Motivated by a universal similarity relation on the individuals, we propose a new selection scheme, which is uniform in the fitness values. It generates selection pressure toward sparsely populated fitness regions, not necessarily toward higher fitness, as is the case for all other selection schemes. We show analytically on a simple example that the new selection scheme can be much more effective than standard selection schemes. We also propose a new deletion scheme which achieves a similar result via deletion and show how such a scheme preserves genetic diversity more effectively than standard approaches. We compare the performance of the new schemes to tournament selection and random deletion on an artificial deceptive problem and a range of NP hard problems: traveling salesman, set covering, and satisfiability

Distribution of mutual information from complete and incomplete data

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sample-to-population inferential approaches. This paper deals with the posterior distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean, and analytical approximations for the variance, skewness and kurtosis are derived. These approximations have a guaranteed accuracy level of the order O(n i3 ), where n is the sample size. Leading order approximations for the mean and the variance are derived in the case of incomplete samples. The derived analytical expressions allow the distribution of mutual information to be approximated reliably and quickly. In fact, the derived expressions can be computed with the same order of complexity needed for descriptive mutual information. This makes the distribution of mutual information become a concrete alternative to descriptive mutual information in many applications which would beneflt from moving to the inductive side. Some of these prospective applications are discussed, and one of them, namely feature selection, is shown to perform signiflcantly better when inductive mutual information is used.

Self-Optimizing and Pareto-Optimal Policies in General Environments Based on Bayes-Mixtures

The problem of making sequential decisions in unknown probabilistic environments is studied. In cycle t action yt results in perception xt and reward rt, where all quantities in general may depend on the complete history. The perception xt and reward rt are sampled from the (reactive) environmental probability distribution ?. This very general setting includes, but is not limited to, (partial observable, k-th order) Markov decision processes. Sequential decision theory tells us how to act in order to maximize the total expected reward, called value, if ? is known. Reinforcement learning is usually used if ? is unknown. In the Bayesian approach one defines a mixture distribution ? as a weighted sum of distributions ? ?M, where M is any class of distributions including the true environment ?. We show that the Bayes-optimal policy p? based on the mixture ? is self-optimizing in the sense that the average value converges asymptotically for all ??M to the optimal value achieved by the (infeasible) Bayes-optimal policy p? which knows ? in advance. We show that the necessary condition that M admits self-optimizing policies at all, is also sufficient. No other structural assumptions are made on M. As an example application, we discuss ergodic Markov decision processes, which allow for self-optimizing policies. Furthermore, we show that p? is Pareto-optimal in the sense that there is no other policy yielding higher or equal value in all environments ? ?M and a strictly higher value in at least one.

Feature Reinforcement Learning: Part I. Unstructured MDPs

Feature Reinforcement Learning: Part I. Unstructured MDPs General-purpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and non-Markovian. On the other hand, reinforcement learning is well-developed for small finite state Markov decision processes (MDPs). Up to now, extracting the right state representations out of bare observations, that is, reducing the general agent setup to the MDP framework, is an art that involves significant effort by designers. The primary goal of this work is to automate the reduction process and thereby significantly expand the scope of many existing reinforcement learning algorithms and the agents that employ them. Before we can think of mechanizing this search for suitable MDPs, we need a formal objective criterion. The main contribution of this article is to develop such a criterion. I also integrate the various parts into one learning algorithm. Extensions to more realistic dynamic Bayesian networks are developed in Part II (Hutter, 2009c). The role of POMDPs is also considered there.