# Inexact Online Proximal Mirror Descent for time-varying composite optimization

arXiv: https://arxiv.org/abs/2304.04710 · HTML: https://mlsanity.com/paper/2304.04710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2023.

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

- [The Hidden Cost of Approximation in Online Mirror Descent](https://mlsanity.com/paper/2511.22283/) (2025)

## Abstract (arXiv)

In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We obtain sharp estimates on the dynamic regret of the algorithm when the regular part of the cost is convex and smooth. If the Bregman distance is given by the Euclidean distance, our result also improves the previous work in two ways: (i) We establish a sharper regret bound compared to the previous work in the sense that our estimate does not involve O(T) term appearing in that work. (ii) We also obtain the result when the domain is the whole space ℝn, whereas the previous work was obtained only for bounded domains. We also provide numerical tests for problems involving the errors in the gradient and proximal operator.