Online convex optimization in the random order model

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Online Convex Optimization (OCO) is a powerful framework for sequential prediction, portraying the natural uncertainty inherent in data-streams as though the data were generated by an almost omniscient adversary. However, this view, which is often too pessimistic for real-world data, comes with a price. The complexity of solving many important online tasks in this adversarial framework becomes much worse than that of their offline and even stochastic counterparts. In this work we consider a natural random-order version of the OCO model, in which the adversary can choose the set of loss functions, but does not get to choose the order in which they are supplied to the learner; Instead, they are observed in uniformly random order. Focusing on two important families of online tasks, one in which the cumulative loss function is strongly convex (though individual loss functions may not even be convex), and the other being online k-PCA, we show that under standard well-conditioned-data assumptions, standard online gradient descent (OGD) methods become much more efficient in the random-order model. In particular, for the first group of tasks OGD guarantees poly-logarithmic regret. In the case of online k-PCA, OGD guarantees sublinear regret using only a rank-k SVD on each iteration and memory linear in the size of the solution.

Original languageEnglish
Title of host publication37th International Conference on Machine Learning, ICML 2020
EditorsHal Daume, Aarti Singh
Number of pages10
ISBN (Electronic)9781713821120
StatePublished - 2020
Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
Duration: 13 Jul 202018 Jul 2020

Publication series

Name37th International Conference on Machine Learning, ICML 2020


Conference37th International Conference on Machine Learning, ICML 2020
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software


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