{"type":"ScholarlyArticle","title":"Interactive Optimal Teaching with Unknown Learners","authors":[{"name":"Francisco S. Melo","slug":"francisco-s-melo","given":"Francisco S.","family":"Melo","affiliation":"INESC-ID , Instituto Superior Técnico , Universidade de Lisboa , Lisbon , Portugal"},{"name":"Carla Guerra","slug":"carla-guerra","given":"Carla","family":"Guerra","affiliation":"INESC-ID , Instituto Superior Técnico , Universidade de Lisboa , Lisbon , Portugal"},{"name":"Manuel Lopes","slug":"manuel-lopes","given":"Manuel","family":"Lopes","affiliation":"INESC-ID , Instituto Superior Técnico , Universidade de Lisboa , Lisbon , Portugal"}],"abstract":"This paper introduces a new approach for machine teaching that\r\npartly addresses the (unavoidable) mismatch between what the\r\nteacher assumes about the learning process of the student and the\r\nactual process. We analyze several situations in which such mismatch\r\ntakes place, including when the student?s learning algorithm\r\nis known but the corresponding parameters are not, and when the\r\nlearning algorithm itself is not known. Our analysis is focused on\r\nthe case of a Bayesian Gaussian learner, and we show that, even\r\nin this simple case, the lack of knowledge regarding the student?s\r\nlearning process significantly deteriorates the performance of machine\r\nteaching: while perfect knowledge of the student ensures that\r\nthe target is learned after a finite number of samples, lack of knowledge\r\nthereof implies that the student will only learn asymptotically\r\n(i.e., after an infinite number of samples). We introduce interactivity\r\nas a means to mitigate the impact of imperfect knowledge\r\nand show that, by using interactivity, we are able to recover finite\r\nlearning time, in the best case, or significantly faster convergence,\r\nin the worst case. Finally, we discuss the extension of our analysis\r\nto a classification problem using linear discriminant analysis, and\r\ndiscuss the implications of our results in single- and multi-student\r\nsettings.","doi":"10.24963/ijcai.2018/356","url":"https://ijcai.org/proceedings/2018/356","pdf":"https://ijcai.org/proceedings/2018/0356.pdf","markdown":"https://ijcai.org/proceedings/2018/356.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/356","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":356,"pages":{"first":2567,"last":2573},"keywords":["Machine Learning Applications: Applications of Supervised Learning","Machine Learning: New Problems","Machine Learning Applications: Other Applications"],"videos":[],"references":[{"position":1,"raw":"[Anderson et al., 1995] John Anderson, Albert Corbett, Kenneth Koedinger, and Ray Pelletier. 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