# A Unified Analysis Method for Online Optimization in Normed Vector Space

arXiv: https://arxiv.org/abs/2112.12134 · HTML: https://mlsanity.com/paper/2112.12134/

## Key facts

- Cited by 1 papers 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 (most cited first, 12 of 12)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [Adaptive Online Learning in Dynamic Environments](https://mlsanity.com/paper/1810.10815/) (2018)
- [Online Optimization : Competing with Dynamic Comparators](https://mlsanity.com/paper/1501.06225/) (2015)
- [Dynamic Regret of Convex and Smooth Functions](https://mlsanity.com/paper/2007.03479/) (2020)
- [Dynamical Models and Tracking Regret in Online Convex Programming](https://mlsanity.com/paper/1301.1254/) (2013)
- [Online Learning with Optimism and Delay](https://mlsanity.com/paper/2106.06885/) (2021)
- [A closer look at temporal variability in dynamic online learning](https://mlsanity.com/paper/2102.07666/) (2021)
- [Unifying mirror descent and dual averaging](https://mlsanity.com/paper/1910.13742/) (2019)
- [Online Monotone Games](https://mlsanity.com/paper/1710.07328/) (2017)
- [Online Monotone Optimization](https://mlsanity.com/paper/1608.07888/) (2016)

## Built on by (most cited first, 1 of 1)

- [Optimistic Online Convex Optimization in Dynamic Environments](https://mlsanity.com/paper/2203.14520/) (2022)

## 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.