Draft : September 10 , 2008 Learning Permutations with Exponential Weights ∗
نویسندگان
چکیده
We give an algorithm for the on-line learning of permutations. The algorithm maintains its uncertainty about the target permutation as a doubly stochastic weight matrix, and uses an efficient method for decomposing the weight matrix as a convex combination of permutations to make predictions. The weight matrix is updated by multiplying the current matrix entries by exponential factors, and an iterative procedure is needed to restore double stochasticity. Even though the result of this procedure does not have a closed form, a new analysis approach allows us to prove an optimal (up to small constant factors) bound on the regret our algorithm. This regret bound is significantly better than that of either Kalai and Vempala’s more efficient Follow the Perturbed Leader algorithm or the computationally expensive method of explicitly representing each permutation as an expert.
منابع مشابه
Draft : February 28 , 2008 Learning Permutations with Exponential Weights ∗
We give an algorithm for learning a permutation on-line. The algorithm maintains its uncertainty about the target permutation as a doubly stochastic matrix. This matrix is updated by multiplying the current matrix entries by exponential factors which destroy the doubly stochastic property of the matrix, and an iterative procedure is needed to renormalize the rows and columns. Even though the re...
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