# Stochastic Online Convex Optimization. Application to probabilistic time series forecasting

arXiv: https://arxiv.org/abs/2102.00729 · HTML: https://mlsanity.com/paper/2102.00729/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 1 Feb 2021.

## Builds on (most cited first, 12 of 12)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [MetaGrad: Multiple Learning Rates in Online Learning](https://mlsanity.com/paper/1604.08740/) (2016)
- [Lipschitz Adaptivity with Multiple Learning Rates in Online Learning](https://mlsanity.com/paper/1902.10797/) (2019)
- [Optimal learning with Bernstein Online Aggregation](https://mlsanity.com/paper/1404.1356/) (2014)
- [Online Learning for Time Series Prediction](https://mlsanity.com/paper/1302.6927/) (2013)
- [Combining Adversarial Guarantees and Stochastic Fast Rates in Online Learning](https://mlsanity.com/paper/1605.06439/) (2016)
- [Efficient online algorithms for fast-rate regret bounds under sparsity](https://mlsanity.com/paper/1805.09174/) (2018)
- [Online Learning with Continuous Ranked Probability Score](https://mlsanity.com/paper/1902.10173/) (2019)
- [Aggregation of predictors for nonstationary sub-linear processes and online adaptive forecasting of time varying autoregressive processes](https://mlsanity.com/paper/1404.6769/) (2014)
- [Kalman Recursions Aggregated Online](https://mlsanity.com/paper/2002.12173/) (2020)

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

- [Online PAC-Bayes Learning](https://mlsanity.com/paper/2206.00024/) (2022)
- [Learning from time-dependent streaming data with online stochastic algorithms](https://mlsanity.com/paper/2205.12549/) (2022)
- [Structured Prediction in Online Learning](https://mlsanity.com/paper/2406.12366/) (2024)
- [When Lower-Order Terms Dominate: Adaptive Expert Algorithms for Heavy-Tailed Losses](https://mlsanity.com/paper/2506.01722/) (2025)
- [Online (Non-)Convex Learning via Tempered Optimism](https://mlsanity.com/paper/2301.07530/) (2023)
- [Online Learning Approach for Survival Analysis](https://mlsanity.com/paper/2402.05145/) (2024)
- [An hybrid stochastic Newton algorithm for logistic regression](https://mlsanity.com/paper/2512.01790/) (2025)
- [High-Probability Minimax Adaptive Estimation in Besov Spaces via Online-to-Batch](https://mlsanity.com/paper/2602.11747/) (2026)

## Abstract (arXiv)

We introduce a general framework of stochastic online convex optimization to obtain fast-rate stochastic regret bounds. We prove that algorithms such as online newton steps and a scale-free 10 version of Bernstein online aggregation achieve best-known rates in unbounded stochastic settings. We apply our approach to calibrate parametric probabilistic forecasters of non-stationary sub-gaussian time series. Our fast-rate stochastic regret bounds are any-time valid. Our proofs combine self-bounded and Poissonnian inequalities for martingales and sub-gaussian random variables, respectively, under a stochastic exp-concavity assumption.