### 抜粋

We consider an on-line learning model of rational choice, in which the goal of an agent is to choose its actions so as to maximize the number of successes, while learning about its reacting environment through those very actions. In particular, we consider a model of tennis play, in which the only actions that the player can take are a `pass' and a `lob,' and the opponent is modeled by two linear (probabilistic) functions f_{L}(r) = a_{1}r+b_{1} and f_{P}(r) = a_{2}r+b_{2}, specifying the probability that a lob (and a pass, respectively) will win a point when the proportion of lobs in the past trials is r. We measure the performance of a player in this model by its expected regret, namely how many less points it expects to win as compared to the ideal player (one that knows the two probabilistic functions) as a function of t, the total number of trials, which is unknown to the player a priori. Assuming that the probabilistic functions satisfy the matching shoulder condition, i.e. f_{L}(0) = f_{P}(1), we obtain a variety of upper bounds for assumptions and restrictions of varying degrees, ranging from O(log t), O(t^{1/3}), O(t^{ 1/2 }), O(t^{3/5}), O(t^{2/3}) to O(t^{5/7}) as well as a matching lower bound of order Ω(log t) for the most restrictive case. When the total number of trials t is given to the player in advance, the upper bounds can be improved significantly.

元の言語 | 英語 |
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ホスト出版物のタイトル | Proc 6 Annu ACM Conf Comput Learn Theory |

出版者 | Publ by ACM |

ページ | 422-428 |

ページ数 | 7 |

ISBN（印刷物） | 0897916115, 9780897916110 |

DOI | |

出版物ステータス | 出版済み - 1993 |

イベント | Proceedings of the 6th Annual ACM Conference on Computational Learning Theory - Santa Cruz, CA, USA 継続期間: 7 26 1993 → 7 28 1993 |

### 出版物シリーズ

名前 | Proc 6 Annu ACM Conf Comput Learn Theory |
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### その他

その他 | Proceedings of the 6th Annual ACM Conference on Computational Learning Theory |
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市 | Santa Cruz, CA, USA |

期間 | 7/26/93 → 7/28/93 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

## これを引用

*Proc 6 Annu ACM Conf Comput Learn Theory*(pp. 422-428). (Proc 6 Annu ACM Conf Comput Learn Theory). Publ by ACM. https://doi.org/10.1145/168304.168389