{"title":"The Asymptotic Cost of Complexity","authors":"Martin W Cripps","doi":"arxiv-2408.14949","DOIUrl":null,"url":null,"abstract":"We propose a measure of learning efficiency for non-finite state spaces. We\ncharacterize the complexity of a learning problem by the metric entropy of its\nstate space. We then describe how learning efficiency is determined by this\nmeasure of complexity. This is, then, applied to two models where agents learn\nhigh-dimensional states.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - ECON - Theoretical Economics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.14949","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a measure of learning efficiency for non-finite state spaces. We
characterize the complexity of a learning problem by the metric entropy of its
state space. We then describe how learning efficiency is determined by this
measure of complexity. This is, then, applied to two models where agents learn
high-dimensional states.
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