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AIXI
AIXI is a theoretical mathematical formalism for artificial general intelligence. It combines Solomonoff induction with sequential decision theory. AIXI was first proposed by Marcus Hutter in 2000 and several results regarding AIXI are proved in Hutter's 2005 book ''Universal Artificial Intelligence''. AIXI is a reinforcement learning (RL) agent. It maximizes the expected total rewards received from the environment. Intuitively, it simultaneously considers every computable hypothesis (or environment). In each time step, it looks at every possible program and evaluates how many rewards that program generates depending on the next action taken. The promised rewards are then weighted by the subjective belief that this program constitutes the true environment. This belief is computed from the length of the program: longer programs are considered less likely, in line with Occam's razor. AIXI then selects the action that has the highest expected total reward in the weighted sum of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solomonoff Induction
Solomonoff's theory of inductive inference is a mathematical proof that if a universe is generated by an algorithm, then observations of that universe, encoded as a dataset, are best predicted by the smallest executable archive of that dataset. This formalization of Occam's razorJJ McCall. Induction: From Kolmogorov and Solomonoff to De Finetti and Back to Kolmogorov – Metroeconomica, 2004 – Wiley Online Library.D Stork. Foundations of Occam's razor and parsimony in learning from ricoh.com – NIPS 2001 Workshop, 2001A.N. Soklakov. Occam's razor as a formal basis for a physical theorfrom arxiv.org– Foundations of Physics Letters, 2002 – SpringerM Hutter. On the existence and convergence of computable universal priorarxiv.org– Algorithmic Learning Theory, 2003 – Springer for induction was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marcus Hutter
Marcus Hutter (born April 14, 1967 in Munich) is DeepMind Senior Scientist researching the mathematical foundations of artificial general intelligence. He is on leave from his professorship at the ANU College of Engineering and Computer Science of the Australian National University in Canberra, Australia. Hutter studied physics and computer science at the Technical University of Munich. In 2000 he joined Jürgen Schmidhuber's group at the Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (Dalle Molle Institute for Artificial Intelligence Research) in Manno, Switzerland. With others, he developed a mathematical theory of artificial general intelligence. His book ''Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability'' was published by Springer in 2005. Research In 2002, Hutter, with Jürgen Schmidhuber and Shane Legg, developed and published a mathematical theory of artificial general intelligence, AIXI, based on idealised in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial General Intelligence
Artificial general intelligence (AGI) is the ability of an intelligent agent to understand or learn any intellectual task that a human being can. It is a primary goal of some artificial intelligence research and a common topic in science fiction and futures studies. AGI is also called strong AI,: Kurzweil describes strong AI as "machine intelligence with the full range of human intelligence." full AI, or general intelligent action, although some academic sources reserve the term "strong AI" for computer programs that experience sentience or consciousness. Strong AI contrasts with '' weak AI'' (or ''narrow AI''), which is not intended to have general cognitive abilities; rather, weak AI is any program that is designed to solve exactly one problem. (Academic sources reserve "weak AI" for programs that do not experience consciousness or do not have a mind in the same sense people do.) A 2020 survey identified 72 active AGI R&D projects spread across 37 countries. Characteristics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel Machine
A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way. It uses a recursive self-improvement protocol in which it rewrites its own code when it can prove the new code provides a better strategy. The machine was invented by Jürgen Schmidhuber (first proposed in 2003), but is named after Kurt Gödel who inspired the mathematical theories. The Gödel machine is often discussed when dealing with issues of meta-learning, also known as "learning to learn." Applications include automating human design decisions and transfer of knowledge between multiple related tasks, and may lead to design of more robust and general learning architectures. Though theoretically possible, no full implementation has been created. The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence. Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixture (probability)
In probability theory and statistics, a mixture is a probabilistic combination of two or more probability distributions. The concept arises mostly in two contexts: :* A mixture defining a new probability distribution from some existing ones, as in a mixture distribution or a compound distribution. Here a major problem often is to derive the properties of the resulting distribution. :* A mixture used as a statistical model such as is often used for statistical classification. The model may represent the population from which observations arise as a mixture of several components, and the problem is that of a mixture model, in which the task is to infer from which of a ''discrete'' set of sub-populations each observation originated. See also * Mixture distribution * Compound distribution * Mixture model In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pac-Man
originally called ''Puck Man'' in Japan, is a 1980 maze action video game developed and released by Namco for arcades. In North America, the game was released by Midway Manufacturing as part of its licensing agreement with Namco America. The player controls Pac-Man, who must eat all the dots inside an enclosed maze while avoiding four colored ghosts. Eating large flashing dots called "Power Pellets" causes the ghosts to temporarily turn blue, allowing Pac-Man to eat them for bonus points. Game development began in early 1979, directed by Toru Iwatani with a nine-man team. Iwatani wanted to create a game that could appeal to women as well as men, because most video games of the time had themes of war or sports. Although the inspiration for the Pac-Man character was the image of a pizza with a slice removed, Iwatani has said he also rounded out the Japanese character for mouth, kuchi ( ja, 口). The in-game characters were made to be cute and colorful to appeal to younger p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Observable System
A partially observable system is one in which the entire state of the system is not fully visible to an external sensor. In a partially observable system the observer may utilise a memory system in order to add information to the observer's understanding of the system.Peter Norvig, Sebastian Thrun. UdacityIntroduction to Artificial Intelligence/ref> An example of a partially observable system would be a card game in which some of the cards are discarded into a pile face down. In this case the observer is only able to view their own cards and potentially those of the dealer. They are not able to view the face-down (used) cards, nor the cards that will be dealt at some stage in the future. A memory system can be used to remember the previously dealt cards that are now on the used pile. This adds to the total sum of knowledge that the observer can use to make decisions. In contrast, a fully observable system would be that of chess. In chess (apart from the 'who is moving next' st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context Tree Weighting
The context tree weighting method (CTW) is a lossless compression and prediction algorithm by . The CTW algorithm is among the very few such algorithms that offer both theoretical guarantees and good practical performance (see, e.g. ). The CTW algorithm is an “ ensemble method”, mixing the predictions of many underlying variable order Markov model In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Mark ...s, where each such model is constructed using zero-order conditional probability ''estimators''. References * * * External links Relevant CTW papers and implementationsCTW Official Homepage Lossless compression algorithms {{comp-sci-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undecidable Problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run. Background A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns ''yes''. These inputs can be natural numbers, but also other values of some other kind, such as strings of a formal language. Using some encoding, such as a Gödel numbering, the strings can be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set of natural numbers. To keep the formal definition simple, it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto Optimality
Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related: * Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. * A situation is called Pareto-dominated if there exists a possible Pareto improvement. * A situation is called Pareto-optimal or Pareto-efficient if no change could lead to improved satisfaction for some agent without some other agent losing or, equivalently, if there is no scope for further Pareto improvement. The Pareto front (also called Pareto frontier or Pareto set) is the set of all Pareto-efficient situations. Pareto originally used the word "optimal" for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
