A tale of two metrics: Simultaneous bounds on competitiveness and regret

Lachlan L.H. Andrew, Siddharth Barman, Katrina Ligett, Minghong Lin, Adam Meyerson, Alan Roytman, Adam Wierman

Research output: Contribution to journalConference articlepeer-review

35 Scopus citations


We consider algorithms for "smoothed online convex optimization" problems, a variant of the class of online convex optimization problems that is strongly related to metrical task systems. Prior literature on these problems has focused on two performance metrics: regret and the competitive ratio. There exist known algorithms with sublinear regret and known algorithms with constant competitive ratios; however, no known algorithm achieves both simultaneously. We show that this is due to a fundamental incompatibility between these two metrics - no algorithm (deterministic or randomized) can achieve sublinear regret and a constant competitive ratio, even in the case when the objective functions are linear. However, we also exhibit an algorithm that, for the important special case of one dimensional decision spaces, provides sublinear regret while maintaining a competitive ratio that grows arbitrarily slowly.

Original languageEnglish
Pages (from-to)741-763
Number of pages23
JournalProceedings of Machine Learning Research
StatePublished - 2013
Externally publishedYes
Event26th Conference on Learning Theory, COLT 2013 - Princeton, NJ, United States
Duration: 12 Jun 201314 Jun 2013


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