We consider the problem of dynamically apportioning resources among a set of options in a worst-case online framework. The model we investigate is a generalization of the well studied online learning model. In particu...
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We consider the problem of dynamically apportioning resources among a set of options in a worst-case online framework. The model we investigate is a generalization of the well studied online learning model. In particular, we allow the learner to see as additional information how high the risk of each option is. This assumption is natural in many applications like horse-race betting, where gamblers know odds for all options before placing bets. We apply Vovk's aggregating algorithm to this problem and give a tight performance bound. The results support our intuition that it is safe to bet more on low-risk options. Surprisingly, the loss bound of the algorithm does not depend on the values of relatively small risks.
Helmbold and Schapire gave an on-line prediction algorithm that, when given an unpruned decision tree, produces predictions not much worse than the predictions made by the best pruning of the given decision tree. In t...
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Helmbold and Schapire gave an on-line prediction algorithm that, when given an unpruned decision tree, produces predictions not much worse than the predictions made by the best pruning of the given decision tree. In this paper, we give two new on-line algorithms. The first algorithm is based on the observation that finding the best pruning can be efficiently solved by a dynamic programming in the "batch" setting where all the data to be predicted are given in advance. This algorithm works well for a wide class of Loss functions, whereas the one given by Helmbold and Schapire is only described for the absolute loss function. Moreover, the algorithm given in this paper is so simple and general that it could be applied to many other on-line optimization problems solved by dynamic programming. We also explore the second algorithm that is competitive not only with the best pruning but also with the best prediction values which are associated with nodes in the decision tree. In this setting, a greatly simplified algorithm is given for the absolute loss function. It can be easily generalized to the case where, instead of using decision trees, data are classified in some arbitrarily fixed manner. (C) 2001 Elsevier Science B.V. All rights reserved.
Helmbold and Schapire gave an on-line prediction algorithm that, when given an unpruned decision tree, produces predictions not much worse than the predictions made by the best pruning of the given decision tree. In t...
详细信息
Helmbold and Schapire gave an on-line prediction algorithm that, when given an unpruned decision tree, produces predictions not much worse than the predictions made by the best pruning of the given decision tree. In this paper, we give two new on-line algorithms. The first algorithm is based on the observation that finding the best pruning can be efficiently solved by a dynamic programming in the "batch" setting where all the data to be predicted are given in advance. This algorithm works well for a wide class of Loss functions, whereas the one given by Helmbold and Schapire is only described for the absolute loss function. Moreover, the algorithm given in this paper is so simple and general that it could be applied to many other on-line optimization problems solved by dynamic programming. We also explore the second algorithm that is competitive not only with the best pruning but also with the best prediction values which are associated with nodes in the decision tree. In this setting, a greatly simplified algorithm is given for the absolute loss function. It can be easily generalized to the case where, instead of using decision trees, data are classified in some arbitrarily fixed manner. (C) 2001 Elsevier Science B.V. All rights reserved.
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