From PAC to Instance-Optimal Sample Complexity in the Plackett-Luce Model

Jul 12, 2020



We consider PAC learning a good item from k-subsetwise feedback sampled from a Plackett-Luce probability model, with instance-dependent sample complexity performance. In the setting where subsets of a fixed size can be tested and top-ranked feedback is made available to the learner, we give an optimal instance-dependent algorithm with a sample complexity bound for PAC best arm identification algorithm of O(Θ_[k]/k∑_i = 2^nmax(1,1/Δ_i^2) lnk/δ(ln1/Δ_i)), Δ_i being the Plackett-Luce parameter gap between the best and the i^th best item, and Θ_[k] is the sum of the Plackett-Luce parameters for top-k items. The algorithm is based on a wrapper around a PAC winner-finding algorithm with weaker performance guarantees to adapt to the hardness of the input instance. The sample complexity is also shown to be multiplicatively better depending on the length of rank-ordered feedback available in each subset-wise play. We show optimality of our algorithms with matching sample complexity lower bounds. We next address the winner-finding problem in Plackett-Luce models in the fixed-budget setting with instance dependent upper and lower bounds on the misidentification probability, of Ω((-2 Δ̃Q) ) for a given budget Q, where Δ̃ is an explicit instance-dependent problem complexity parameter. Numerical performance results are also reported for the algorithms.



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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