# Online Convex Optimization with Long Term Constraints for Predictable Sequences

arXiv: https://arxiv.org/abs/2210.16735 · HTML: https://mlsanity.com/paper/2210.16735/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [Adaptive Algorithms for Online Convex Optimization with Long-term Constraints](https://mlsanity.com/paper/1512.07422/) (2015)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Online convex optimization for cumulative constraints](https://mlsanity.com/paper/1802.06472/) (2018)
- [Regret and Cumulative Constraint Violation Analysis for Online Convex Optimization with Long Term Constraints](https://mlsanity.com/paper/2106.05135/) (2021)
- [Online Learning with Imperfect Hints](https://mlsanity.com/paper/2002.04726/) (2020)

## Built on by (most cited first, 2 of 2)

- [An Optimistic Algorithm for Online Convex Optimization with Adversarial Constraints](https://mlsanity.com/paper/2412.08060/) (2024)
- [Distributed Online Convex Optimization with Nonseparable Costs and Constraints](https://mlsanity.com/paper/2602.10452/) (2026)

## Abstract (arXiv)

In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called it OCO with long term constraints. Long term constraints are introduced typically as an alternative to reduce the complexity of the projection at every update step in online optimization. While many algorithmic advances have been made towards online optimization with long term constraints, these algorithms typically assume that the sequence of cost functions over a certain T finite steps that determine the cost to the online learner are adversarially generated. In many circumstances, the sequence of cost functions may not be unrelated, and thus predictable from those observed till a point of time. In this paper, we study the setting where the sequences are predictable. We present a novel online optimization algorithm for online optimization with long term constraints that can leverage such predictability. We show that, with a predictor that can supply the gradient information of the next function in the sequence, our algorithm can achieve an overall regret and constraint violation rate that is strictly less than the rate that is achievable without prediction.