Related papers: On the Computability of AIXI
Solomonoff induction is held as a gold standard for learning, but it is known to be incomputable. We quantify its incomputability by placing various flavors of Solomonoff's prior M in the arithmetical hierarchy. We also derive computability…
Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction…
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…
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…
AIXI is a widely studied model of artificial general intelligence (AGI) based upon principles of induction and reinforcement learning. However, AIXI is fundamentally classical in nature - as are the environments in which it is modelled.…
Artificial general intelligence (AGI) may herald our extinction, according to AI safety research. Yet claims regarding AGI must rely upon mathematical formalisms -- theoretical agents we may analyse or attempt to build. AIXI appears to be…
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents.…
In recent years we observed rapid and significant advancements in artificial intelligence (A.I.). So much so that many wonder how close humanity is to developing an A.I. model that can achieve human level of intelligence, also known as…
We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the…
This paper presents Unlimited Computable AI, or UCAI, that is a family of computable variants of AIXI. UCAI is more powerful than AIXItl, that is a conventional family of computable variants of AIXI, in the following ways: 1) UCAI supports…
Algorithmic Information Theory has inspired intractable constructions of general intelligence (AGI), and undiscovered tractable approximations are likely feasible. Reinforcement Learning (RL), the dominant paradigm by which an agent might…
There are a variety of results in the literature proving forms of computability for topological entropy and pressure on subshifts. In this work, we prove two quite general results, showing that topological pressure is always computable from…
We identify principles characterizing Solomonoff Induction by demands on an agent's external behaviour. Key concepts are rationality, computability, indifference and time consistency. Furthermore, we discuss extensions to the full AI case…
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.…
We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter…
We give a brief introduction to the AIXI model, which unifies and overcomes the limitations of sequential decision theory and universal Solomonoff induction. While the former theory is suited for active agents in known environments, the…
Solomonoff Induction is an optimal-in-the-limit unbounded algorithm for sequence prediction, representing a Bayesian mixture of every computable probability distribution and performing close to optimally in predicting any computable…
Solomonoff's inductive learning model is a powerful, universal and highly elegant theory of sequence prediction. Its critical flaw is that it is incomputable and thus cannot be used in practice. It is sometimes suggested that it may still…
A big open question of algorithmic information theory is the choice of the universal Turing machine (UTM). For Kolmogorov complexity and Solomonoff induction we have invariance theorems: the choice of the UTM changes bounds only by a…
It is known that the normalized algorithmic information distance $N$ is not computable and not semicomputable. We show that for all $\epsilon < 1/2$, there exist no semicomputable functions that differ from $N$ by at most~$\epsilon$.…