A Unified Analysis Method for Online Optimization in Normed Vector Space
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Abstract (arXiv)
This paper studies online optimization from a high-level unified theoretical perspective. We not only generalize both Optimistic-DA and Optimistic-MD in normed vector space, but also unify their analysis methods for dynamic regret. Regret bounds are the tightest possible due to the introduction of φ-convex. As instantiations, regret bounds of normalized exponentiated subgradient and greedy/lazy projection are better than the currently known optimal results. By replacing losses of online game with monotone operators, and extending the definition of regret, namely regretn, we extend online convex optimization to online monotone optimization.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 12 of its 39 references that are in the map. First posted on arXiv 22 Dec 2021.
Builds on
12 of 39 references.
References · 12
- 2019Introduction to Online Convex Optimizationcited by 803
- 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 417
- 2015Fast Convergence of Regularized Learning in Gamescited by 150
- 2018Adaptive Online Learning in Dynamic Environmentscited by 133
- 2015Online Optimization : Competing with Dynamic Comparatorscited by 99
- 2020Dynamic Regret of Convex and Smooth Functionscited by 90
- 2013Dynamical Models and Tracking Regret in Online Convex Programmingcited by 43
- 2021Online Learning with Optimism and Delaycited by 33
- 2021A closer look at temporal variability in dynamic online learningcited by 13
- 2019Unifying mirror descent and dual averagingcited by 8
- 2017Online Monotone Gamescited by 3
- 2016Online Monotone Optimizationcited by 2
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Citing papers per year: 2022: 1.
1 paper.