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Recently, it has been reported that chaotically oscillating ultrafast time series from a laser, called laser chaos, provides the ability to solve multi\u2010armed bandit (MAB) problems or decision\u2010making problems at GHz order. Furthermore, it has been confirmed that the negatively correlated time\u2010domain structure of laser chaos contributes to the acceleration of decision\u2010making. However, the underlying mechanism of why decision\u2010making is accelerated by correlated time series is unknown. In this study, we demonstrate a theoretical model to account for accelerating decision\u2010making by correlated time sequence. We first confirm the effectiveness of the negative autocorrelation inherent in time series for solving two\u2010armed bandit problems using Fourier transform surrogate methods. We propose a theoretical model that concerns the correlated time series subjected to the decision\u2010making system and the internal status of the system therein in a unified manner, inspired by correlated random walks. We demonstrate that the performance derived analytically by the theory agrees well with the numerical simulations, which confirms the validity of the proposed model and leads to optimal system design. This study paves the way for improving the effectiveness of correlated time series for decision\u2010making, impacting artificial intelligence and other applications.<\/jats:p>","DOI":"10.1155\/2022\/5205580","type":"journal-article","created":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T21:50:09Z","timestamp":1661464209000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Theory of Acceleration of Decision\u2010Making by Correlated Time Sequences"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9318-1036","authenticated-orcid":false,"given":"Norihiro","family":"Okada","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3003-1935","authenticated-orcid":false,"given":"Tomoki","family":"Yamagami","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6504-1730","authenticated-orcid":false,"given":"Nicolas","family":"Chauvet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5218-0440","authenticated-orcid":false,"given":"Yusuke","family":"Ito","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5638-8022","authenticated-orcid":false,"given":"Mikio","family":"Hasegawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8982-9824","authenticated-orcid":false,"given":"Makoto","family":"Naruse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,8,25]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41566-020-00754-y"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-020-2973-6"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1186\/s43593-021-00002-y"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41566-020-00716-4"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.5108912"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.1998.712192"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-017-08585-8"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/JSTQE.2019.2929217"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1364\/OPTICA.5.000756"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-018-29117-y"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-020-58541-2"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1587\/nolta.13.84"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1587\/nolta.13.72"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-020-66441-8"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/TMC.2010.65"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/8877660"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.1049\/el:19990754"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2003.812605"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1587\/transcom.2016NEI0002"},{"key":"e_1_2_10_20_2","first-page":"849","article-title":"Construction of optimal chaotic spreading sequence using Lebesgue spectrum filter","volume":"85","author":"Umeno K.","year":"2002","journal-title":"IEICE Trans. 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