{"title":"赌博和分裂","authors":"Cédric Bleuler, A. Lapidoth, Christoph Pfister","doi":"10.1109/ISIT.2019.8849800","DOIUrl":null,"url":null,"abstract":"For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly’s logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived, and the connection to the Rényi divergence is shown. Optimal strategies are also derived when the gambler has some side information; this setting leads to a novel conditional Rényi divergence.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"18 1","pages":"2214-2218"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Gambling and Rényi Divergence\",\"authors\":\"Cédric Bleuler, A. Lapidoth, Christoph Pfister\",\"doi\":\"10.1109/ISIT.2019.8849800\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly’s logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived, and the connection to the Rényi divergence is shown. Optimal strategies are also derived when the gambler has some side information; this setting leads to a novel conditional Rényi divergence.\",\"PeriodicalId\":6708,\"journal\":{\"name\":\"2019 IEEE International Symposium on Information Theory (ISIT)\",\"volume\":\"18 1\",\"pages\":\"2214-2218\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2019 IEEE International Symposium on Information Theory (ISIT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2019.8849800\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 IEEE International Symposium on Information Theory (ISIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2019.8849800","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly’s logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived, and the connection to the Rényi divergence is shown. Optimal strategies are also derived when the gambler has some side information; this setting leads to a novel conditional Rényi divergence.
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