# Introduction to Online Convex Optimization

arXiv: https://arxiv.org/abs/1909.05207 · HTML: https://mlsanity.com/paper/1909.05207/

## Key facts

- Cited by 803 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2019.

## Built on by (most cited first, 30 of 803)

- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
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- [The Road Less Scheduled](https://mlsanity.com/paper/2405.15682/) (2024)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be](https://mlsanity.com/paper/2304.13960/) (2023)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Learning Curve Theory](https://mlsanity.com/paper/2102.04074/) (2021)
- [Reward is enough for convex MDPs](https://mlsanity.com/paper/2106.00661/) (2021)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Online Continual Learning with Natural Distribution Shifts: An Empirical Study with Visual Data](https://mlsanity.com/paper/2108.09020/) (2021)
- [Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization](https://mlsanity.com/paper/2112.14368/) (2021)
- [It's All Connected: A Journey Through Test-Time Memorization, Attentional Bias, Retention, and Online Optimization](https://mlsanity.com/paper/2504.13173/) (2025)
- [Active Preference Optimization for Sample Efficient RLHF](https://mlsanity.com/paper/2402.10500/) (2024)
- [Making SGD Parameter-Free](https://mlsanity.com/paper/2205.02160/) (2022)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Public Data-Assisted Mirror Descent for Private Model Training](https://mlsanity.com/paper/2112.00193/) (2021)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Parameter-free Mirror Descent](https://mlsanity.com/paper/2203.00444/) (2022)
- [Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion](https://mlsanity.com/paper/2302.03775/) (2023)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [A Unifying Framework for Online Optimization with Long-Term Constraints](https://mlsanity.com/paper/2209.07454/) (2022)
- [An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning](https://mlsanity.com/paper/2308.00788/) (2023)
- [Quantifying the Gain in Weak-to-Strong Generalization](https://mlsanity.com/paper/2405.15116/) (2024)
- [Optimal Dynamic Regret in Exp-Concave Online Learning](https://mlsanity.com/paper/2104.11824/) (2021)
- [Regret and Cumulative Constraint Violation Analysis for Online Convex Optimization with Long Term Constraints](https://mlsanity.com/paper/2106.05135/) (2021)
- [SGD Generalizes Better Than GD (And Regularization Doesn't Help)](https://mlsanity.com/paper/2102.01117/) (2021)

## Abstract (arXiv)

This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.