# O(√T) Static Regret and Instance Dependent Constraint Violation for Constrained Online Convex Optimization

arXiv: https://arxiv.org/abs/2502.05019 · HTML: https://mlsanity.com/paper/2502.05019/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2025.

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

- [Convex Optimization with Nested Evolving Feasible Sets](https://mlsanity.com/paper/2605.07386/) (2026)
- [Multi-Objective textitmin-max Online Convex Optimization](https://mlsanity.com/paper/2510.13560/) (2025)

## Abstract (arXiv)

The constrained version of the standard online convex optimization (OCO) framework, called COCO is considered, where on every round, a convex cost function and a convex constraint function are revealed to the learner after it chooses the action for that round. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV). An algorithm is proposed that guarantees a static regret of O(√T) and a CCV of mincV, O(√Tlog T) , where cV depends on the distance between the consecutively revealed constraint sets, the shape of constraint sets, dimension of action space and the diameter of the action space. For special cases of constraint sets, cV=O(1). Compared to the state of the art results, static regret of O(√T) and CCV of O(√Tlog T), that were universal, the new result on CCV is instance dependent, which is derived by exploiting the geometric properties of the constraint sets.