摘要翻译:
我们考虑一个与未知环境交互的agent。环境是将自然数映射到自然数的函数;agent关于环境的假设集包含所有这些函数,这些函数是可计算的,并且与有限组已知的输入-输出对相容,并且agent为每一个这样的假设分配一个正的概率。我们不要求这个概率分布是可计算的,但它必须在下面有一个正的可计算函数的界限。代理对来自环境的输出具有实用功能。我们证明了如果这个效用函数在绝对值下有界于一个无界的可计算函数,那么任何输入的期望效用是未定义的。这意味着如果一个可计算效用函数是有界的,那么该函数将具有收敛的期望效用。
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英文标题:
《Convergence of Expected Utilities with Algorithmic Probability
Distributions》
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作者:
Peter de Blanc
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最新提交年份:
2007
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分类信息:
一级分类:Computer Science 计算机科学
二级分类:Artificial Intelligence 人工智能
分类描述:Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域,除了视觉、机器人、机器学习、多智能体系统以及计算和语言(自然语言处理),这些领域有独立的学科领域。特别地,包括专家系统,定理证明(尽管这可能与计算机科学中的逻辑重叠),知识表示,规划,和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要:
We consider an agent interacting with an unknown environment. The environment is a function which maps natural numbers to natural numbers; the agent's set of hypotheses about the environment contains all such functions which are computable and compatible with a finite set of known input-output pairs, and the agent assigns a positive probability to each such hypothesis. We do not require that this probability distribution be computable, but it must be bounded below by a positive computable function. The agent has a utility function on outputs from the environment. We show that if this utility function is bounded below in absolute value by an unbounded computable function, then the expected utility of any input is undefined. This implies that a computable utility function will have convergent expected utilities iff that function is bounded.
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PDF链接:
https://arxiv.org/pdf/0712.4318