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Gödel machines: Fully selfreferential optimal universal selfimprovers
 Goertzel and C. Pennachin, Artificial General Intelligence
, 2006
"... Summary. We present the first class of mathematically rigorous, general, fully selfreferential, selfimproving, optimally efficient problem solvers. Inspired by Kurt Gödel’s celebrated selfreferential formulas (1931), such a problem solver rewrites any part of its own code as soon as it has found ..."
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Cited by 25 (12 self)
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Summary. We present the first class of mathematically rigorous, general, fully selfreferential, selfimproving, optimally efficient problem solvers. Inspired by Kurt Gödel’s celebrated selfreferential formulas (1931), such a problem solver rewrites any part of its own code as soon as it has found a proof that the rewrite is useful, where the problemdependent utility function and the hardware and the entire initial code are described by axioms encoded in an initial proof searcher which is also part of the initial code. The searcher systematically and efficiently tests computable proof techniques (programs whose outputs are proofs) until it finds a provably useful, computable selfrewrite. We show that such a selfrewrite is globally optimal—no local maxima!—since the code first had to prove that it is not useful to continue the proof search for alternative selfrewrites. Unlike previous nonselfreferential methods based on hardwired proof searchers, ours not only boasts an optimal order of complexity but can optimally reduce any slowdowns hidden by the O()notation, provided the utility of such speedups is provable at all. 1
Universal Algorithmic Intelligence: A mathematical topdown approach
 Artificial General Intelligence
, 2005
"... Artificial intelligence; algorithmic probability; sequential decision theory; rational ..."
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Cited by 22 (6 self)
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Artificial intelligence; algorithmic probability; sequential decision theory; rational
Gödel Machines: SelfReferential Universal Problem Solvers Making Provably Optimal SelfImprovements
, 2003
"... An old dream of computer scientists is to build an optimally ecient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Gödel's celebrated selfreferential formulas (1931). Our Godel machine's initial software includes an axiomat ..."
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Cited by 16 (7 self)
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An old dream of computer scientists is to build an optimally ecient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Gödel's celebrated selfreferential formulas (1931). Our Godel machine's initial software includes an axiomatic description of: the Godel machine's hardware, the problemspeci c utility function (such as the expected future reward of a robot), known aspects of the environment, costs of actions and computations, and the initial software itself (this is possible without introducing circularity). It also includes a typically suboptimal initial problemsolving policy and an asymptotically optimal proof searcher searching the space of computable proof techniquesthat is, programs whose outputs are proofs. Unlike previous approaches, the selfreferential Gödel machine will rewrite any part of its software, including axioms and proof searcher, as soon as it has found a proof that this will improve its future performance, given its typically limited computational resources. We show that selfrewrites are globally optimalno local minima!since provably none of all the alternative rewrites and proofs (those that could be found by continuing the proof search) are worth waiting for.
The New AI: General & Sound & Relevant for Physics
, 2003
"... Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inducti ..."
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Cited by 15 (9 self)
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Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam's razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse's thesis of the computergenerated universe.
A MonteCarlo AIXI Approximation
, 2009
"... This paper describes a computationally feasible approximation to the AIXI agent, a universal reinforcement learning agent for arbitrary environments. AIXI is scaled down in two key ways: First, the class of environment models is restricted to all prediction suffix trees of a fixed maximum depth. Thi ..."
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Cited by 11 (5 self)
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This paper describes a computationally feasible approximation to the AIXI agent, a universal reinforcement learning agent for arbitrary environments. AIXI is scaled down in two key ways: First, the class of environment models is restricted to all prediction suffix trees of a fixed maximum depth. This allows a Bayesian mixture of environment models to be computed in time proportional to the logarithm of the size of the model class. Secondly, the finitehorizon expectimax search is approximated by an asymptotically convergent Monte Carlo Tree Search technique. This scaled down AIXI agent is empirically shown to be effective on a wide class of toy problem domains, ranging from simple fully observable games to small POMDPs. We explore the limits of this approximate agent and propose a general heuristic framework for scaling this technique to much larger problems.
Contemporary approaches to artificial general intelligence
 Goertzel and C. Pennachin, Artificial General Intelligence
, 2007
"... The vast bulk of the AI field today is concerned with what might be called “narrow AI ” – creating programs that demonstrate intelligence in one or another specialized area, such as chessplaying, medical diagnosis, automobiledriving, algebraic calculation or mathematical theoremproving. Some of t ..."
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Cited by 5 (0 self)
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The vast bulk of the AI field today is concerned with what might be called “narrow AI ” – creating programs that demonstrate intelligence in one or another specialized area, such as chessplaying, medical diagnosis, automobiledriving, algebraic calculation or mathematical theoremproving. Some of these narrow AI programs are extremely successful at what they do. The AI projects discussed in this book, however, are quite different: they are explicitly aimed at artificial general intelligence, at the construction of a software program that can solve a variety of complex problems in a variety of different domains, and that controls itself autonomously, with its own thoughts, worries, feelings, strengths, weaknesses and predispositions. Artificial General Intelligence (AGI) was the original focus of the AI field, but due to the demonstrated difficulty of the problem, not many AI researchers are directly concerned with it anymore. Work on AGI has gotten a bit of a bad reputation, as if creating digital general intelligence were analogous to building a perpetual motion machine. Yet, while the latter is strongly implied
1 The New AI is General & Mathematically Rigorous
"... Summary. Most traditional artificial intelligence (AI) systems of the past decades are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, ..."
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Summary. Most traditional artificial intelligence (AI) systems of the past decades are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam’s razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse’s thesis of the computergenerated universe. We first briefly review the history of AI since Gödel’s 1931 paper, then discuss recent post2000 approaches that are currently transforming general AI research into a formal science.
Continually Adding SelfInvented Problems to the Repertoire: First Experiments with POWERPLAY
"... Abstract—Pure scientists do not only invent new methods to solve given problems. They also invent new problems. The recent POWERPLAY framework formalizes this type of curiosity and creativity in a new, general, yet practical way. To acquire problem solving prowess through playing, POWERPLAYbased ar ..."
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Abstract—Pure scientists do not only invent new methods to solve given problems. They also invent new problems. The recent POWERPLAY framework formalizes this type of curiosity and creativity in a new, general, yet practical way. To acquire problem solving prowess through playing, POWERPLAYbased artificial explorers by design continually come up with the fastest to find, initially novel, but eventually solvable problems. They also continually simplify or speed up solutions to previous problems. We report on results of first experiments with POWERPLAY. A selfdelimiting recurrent neural network (SLIM RNN) is used as a general computational architecture to implement the system’s solver. Its weights can encode arbitrary, selfdelimiting, halting or nonhalting programs affecting both environment (through effectors) and internal states encoding abstractions of event sequences. In openended fashion, our POWERPLAYdriven RNNs learn to become increasingly general problem solvers, continually adding new problem solving procedures to the growing repertoire, exhibiting interesting developmental stages. I.