Efficient minimax strategies for square loss games

Koolen, Wouter M., Malek, Alan, & Bartlett, Peter L. (2014) Efficient minimax strategies for square loss games. In Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N.D., & Weinberger, K.Q. (Eds.) Advances in Neural Information Processing Systems 27 (NIPS 2014), Neural Information Processing Systems Foundation, Inc., Montreal, Quebec, Canada, pp. 3230-3238.

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We consider online prediction problems where the loss between the prediction and the outcome is measured by the squared Euclidean distance and its generalization, the squared Mahalanobis distance. We derive the minimax solutions for the case where the prediction and action spaces are the simplex (this setup is sometimes called the Brier game) and the \ell_2 ball (this setup is related to Gaussian density estimation). We show that in both cases the value of each sub-game is a quadratic function of a simple statistic of the state, with coefficients that can be efficiently computed using an explicit recurrence relation. The resulting deterministic minimax strategy and randomized maximin strategy are linear functions of the statistic.

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ID Code: 82487
Item Type: Conference Paper
Refereed: Yes
Divisions: Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 [please consult the authors]
Deposited On: 12 Mar 2015 23:11
Last Modified: 24 Jun 2017 08:02

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