Minimax Rate for Learning From Pairwise Comparisons in the BTL Model
Jul 12, 2020
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Alex Olshevsky
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Julien Hendrickx
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Venkatesh Saligrama
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About
We consider the problem of learning the qualities w_1, ... , w_n of a collection of items by performing noisy comparisons among them. We assume there is a fixed “comparison graph” and every neighboring pair of items is compared k times. We will study the popular Bradley-Terry-Luce model, where the probability that item i wins a comparison against j equals w_i/(w_i + w_j). We are interested in how the expected error in estimating the vector w = (w_1, ... , w_n) behaves in the regime when the number of comparisons k is large. Our contribution is the determination of the minimax rate up to a constant factor. We show that this rate is achieved by a simple algorithm based on weighted least squares, with weights determined from the empirical outcomes of the comparisons. This algorithm can be implemented in nearly linear time in the total number of comparisons.We consider the problem of learning the qualities w_1, ... , w_n of a collection of items by performing noisy comparisons among them. We assume there is a fixed “comparison graph” and every neighboring pair of items is compared k times. We will study the popular Bradley-Terry-Luce model, where the probability that item i wins a comparison against j equals w_i/(w_i + w_j). We are interested in how the expected error in estimating the vector w = (w_1, ... , w_n) behaves in the regime when the numb…
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About ICML 2020
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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