TY - GEN

T1 - `Lob-pass' problem and an on-line learning model of rational choice

AU - Abe, Naoki

AU - Takeuchi, Jun ichi

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

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U2 - 10.1145/168304.168389

DO - 10.1145/168304.168389

M3 - Conference contribution

AN - SCOPUS:0027843807

SN - 0897916115

SN - 9780897916110

T3 - Proc 6 Annu ACM Conf Comput Learn Theory

SP - 422

EP - 428

BT - Proc 6 Annu ACM Conf Comput Learn Theory

PB - Publ by ACM

T2 - Proceedings of the 6th Annual ACM Conference on Computational Learning Theory

Y2 - 25 July 1993 through 27 July 1993

ER -