# Mixture of Online and Offline Experts for Non-stationary Time Series

arXiv: https://arxiv.org/abs/2202.05996 · HTML: https://mlsanity.com/paper/2202.05996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 12 Feb 2022.

## Builds on (most cited first, 9 of 9)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Adaptive Online Learning in Dynamic Environments](https://mlsanity.com/paper/1810.10815/) (2018)
- [Kitsune: An Ensemble of Autoencoders for Online Network Intrusion Detection](https://mlsanity.com/paper/1802.09089/) (2018)
- [The Optimal Sample Complexity of PAC Learning](https://mlsanity.com/paper/1507.00473/) (2015)
- [MetaGrad: Multiple Learning Rates in Online Learning](https://mlsanity.com/paper/1604.08740/) (2016)
- [Tracking the Best Expert in Non-stationary Stochastic Environments](https://mlsanity.com/paper/1712.00578/) (2017)
- [Concept Drift Adaptation by Exploiting Historical Knowledge](https://mlsanity.com/paper/1702.03500/) (2017)
- [Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learning](https://mlsanity.com/paper/1602.05916/) (2016)

## Abstract (arXiv)

We consider a general and realistic scenario involving non-stationary time series, consisting of several offline intervals with different distributions within a fixed offline time horizon, and an online interval that continuously receives new samples. For non-stationary time series, the data distribution in the current online interval may have appeared in previous offline intervals. We theoretically explore the feasibility of applying knowledge from offline intervals to the current online interval. To this end, we propose the Mixture of Online and Offline Experts (MOOE). MOOE learns static offline experts from offline intervals and maintains a dynamic online expert for the current online interval. It then adaptively combines the offline and online experts using a meta expert to make predictions for the samples received in the online interval. Specifically, we focus on theoretical analysis, deriving parameter convergence, regret bounds, and generalization error bounds to prove the effectiveness of the algorithm.