A Batch-to-Online Transformation under Random-Order Model

• URL: http://arxiv.org/abs/2306.07163v2
• Date: Wed, 25 Oct 2023 23:22:08 GMT
• Title: A Batch-to-Online Transformation under Random-Order Model
• Authors: Jing Dong, Yuichi Yoshida
• Abstract summary: We introduce a transformation framework that can be utilized to develop online algorithms with low $epsilon$-approximate regret. We apply it to various problems, including online $(k,z)$-clustering, online matrix approximation, and online regression. Our algorithm also enjoys low inconsistency, which may be desired in some online applications.
• Score: 23.817140289575377
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a transformation framework that can be utilized to develop online algorithms with low $\epsilon$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that transforms an offline approximation algorithm with low average sensitivity to an online algorithm with low $\epsilon$-approximate regret. We then demonstrate that offline approximation algorithms can be transformed into a low-sensitivity version using a coreset construction method. To showcase the versatility of our approach, we apply it to various problems, including online $(k,z)$-clustering, online matrix approximation, and online regression, and successfully achieve polylogarithmic $\epsilon$-approximate regret for each problem. Moreover, we show that in all three cases, our algorithm also enjoys low inconsistency, which may be desired in some online applications.

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