# `Lob-pass' problem and an on-line learning model of rational choice

8 被引用数 (Scopus)

## 抄録

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 fL(r) = a1r+b1 and fP(r) = a2r+b2, 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. fL(0) = fP(1), we obtain a variety of upper bounds for assumptions and restrictions of varying degrees, ranging from O(log t), O(t1/3), O(t 1/2 ), O(t3/5), O(t2/3) to O(t5/7) 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.

本文言語 英語 Proc 6 Annu ACM Conf Comput Learn Theory Publ by ACM 422-428 7 0897916115, 9780897916110 https://doi.org/10.1145/168304.168389 出版済み - 1993 はい 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

### その他

その他 Proceedings of the 6th Annual ACM Conference on Computational Learning Theory Santa Cruz, CA, USA 7/26/93 → 7/28/93

• 工学（全般）

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