{"title":"具有连续武器的单峰强盗:无平滑的秩序最优后悔","authors":"Richard Combes, A. Proutière, A. Fauquette","doi":"10.1145/3393691.3394225","DOIUrl":null,"url":null,"abstract":"We consider stochastic bandit problems with a continuous set of arms and where the expected reward is a continuous and unimodal function of the arm. For these problems, we propose the Stochastic Polychotomy (SP) algorithms, and derive finite-time upper bounds on their regret and optimization error. We show that, for a class of reward functions, the SP algorithm achieves a regret and an optimization error with optimal scalings, i.e., O(√T) and O(1/√T) (up to a logarithmic factor), respectively.","PeriodicalId":188517,"journal":{"name":"Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Unimodal Bandits with Continuous Arms: Order-optimal Regret without Smoothness\",\"authors\":\"Richard Combes, A. Proutière, A. Fauquette\",\"doi\":\"10.1145/3393691.3394225\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider stochastic bandit problems with a continuous set of arms and where the expected reward is a continuous and unimodal function of the arm. For these problems, we propose the Stochastic Polychotomy (SP) algorithms, and derive finite-time upper bounds on their regret and optimization error. We show that, for a class of reward functions, the SP algorithm achieves a regret and an optimization error with optimal scalings, i.e., O(√T) and O(1/√T) (up to a logarithmic factor), respectively.\",\"PeriodicalId\":188517,\"journal\":{\"name\":\"Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3393691.3394225\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3393691.3394225","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Unimodal Bandits with Continuous Arms: Order-optimal Regret without Smoothness
We consider stochastic bandit problems with a continuous set of arms and where the expected reward is a continuous and unimodal function of the arm. For these problems, we propose the Stochastic Polychotomy (SP) algorithms, and derive finite-time upper bounds on their regret and optimization error. We show that, for a class of reward functions, the SP algorithm achieves a regret and an optimization error with optimal scalings, i.e., O(√T) and O(1/√T) (up to a logarithmic factor), respectively.
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