2021/05/29 by Sinho Chewi, Chewi, Sinho, Patrik Gerber +7 · 1 citation
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2105.14166
openalex publication_date 2021/05/29 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28
We consider the task of generating exact samples from a target distribution, known up to normalization, over a finite alphabet. The classical algorithm for this task is rejection sampling, and although it has been used in practice for decades, there is surprisingly little study of its fundamental limitations. In this work, we study the query complexity of rejection sampling in a minimax framework for various classes of discrete distributions. Our results provide new algorithms for sampling whose complexity scales sublinearly with the alphabet size. When applied to adversarial bandits, we show that a slight modification of the Exp3 algorithm reduces the per-iteration complexity from \mathcal O(K) to \mathcal O(log2 K), where K is the number of arms.