# Unifying mirror descent and dual averaging

arXiv: https://arxiv.org/abs/1910.13742 · HTML: https://mlsanity.com/paper/1910.13742/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

## Built on by (most cited first, 8 of 8)

- [Adaptive Learning in Continuous Games: Optimal Regret Bounds and Convergence to Nash Equilibrium](https://mlsanity.com/paper/2104.12761/) (2021)
- [Parameter-free Stochastic Optimization of Variationally Coherent Functions](https://mlsanity.com/paper/2102.00236/) (2021)
- [Understanding the bias-variance tradeoff of Bregman divergences](https://mlsanity.com/paper/2202.04167/) (2022)
- [Learning Stationary Nash Equilibrium Policies in n-Player Stochastic Games with Independent Chains](https://mlsanity.com/paper/2201.12224/) (2022)
- [Ensembling over Classifiers: a Bias-Variance Perspective](https://mlsanity.com/paper/2206.10566/) (2022)
- [Robust Methods for High-Dimensional Linear Learning](https://mlsanity.com/paper/2208.05447/) (2022)
- [Primal-dual algorithm for contextual stochastic combinatorial optimization](https://mlsanity.com/paper/2505.04757/) (2025)
- [A Unified Analysis Method for Online Optimization in Normed Vector Space](https://mlsanity.com/paper/2112.12134/) (2021)

## Abstract (arXiv)

We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization that combines the advantages of mirror descent and dual averaging. Our preliminary simulation study shows that these new algorithms significantly outperform available methods in some situations.