# Online Optimization in Dynamic Environments

arXiv: https://arxiv.org/abs/1307.5944 · HTML: https://mlsanity.com/paper/1307.5944/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2013.

## Built on by (most cited first, 4 of 4)

- [Unconstrained Online Learning with Unbounded Losses](https://mlsanity.com/paper/2306.04923/) (2023)
- [An Equivalence Between Static and Dynamic Regret Minimization](https://mlsanity.com/paper/2406.01577/) (2024)
- [Dynamic Regret Reduces to Kernelized Static Regret](https://mlsanity.com/paper/2507.05478/) (2025)
- [Dynamic Regret Analysis for Online Meta-Learning](https://mlsanity.com/paper/2109.14375/) (2021)

## Abstract (arXiv)

High-velocity streams of high-dimensional data pose significant "big data" analysis challenges across a range of applications and settings. Online learning and online convex programming play a significant role in the rapid recovery of important or anomalous information from these large datastreams. While recent advances in online learning have led to novel and rapidly converging algorithms, these methods are unable to adapt to nonstationary environments arising in real-world problems. This paper describes a dynamic mirror descent framework which addresses this challenge, yielding low theoretical regret bounds and accurate, adaptive, and computationally efficient algorithms which are applicable to broad classes of problems. The methods are capable of learning and adapting to an underlying and possibly time-varying dynamical model. Empirical results in the context of dynamic texture analysis, solar flare detection, sequential compressed sensing of a dynamic scene, traffic surveillance,tracking self-exciting point processes and network behavior in the Enron email corpus support the core theoretical findings.