# Distributed Online Convex Optimization with Time-Varying Coupled Inequality Constraints

arXiv: https://arxiv.org/abs/1903.04277 · HTML: https://mlsanity.com/paper/1903.04277/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2019.

## Built on by (most cited first, 28 of 28)

- [A Unifying Framework for Online Optimization with Long-Term Constraints](https://mlsanity.com/paper/2209.07454/) (2022)
- [Regret and Cumulative Constraint Violation Analysis for Online Convex Optimization with Long Term Constraints](https://mlsanity.com/paper/2106.05135/) (2021)
- [Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization](https://mlsanity.com/paper/2105.00321/) (2021)
- [Distributed Online Convex Optimization with Adversarial Constraints: Reduced Cumulative Constraint Violation Bounds under Slater's Condition](https://mlsanity.com/paper/2306.00149/) (2023)
- [Projection-free Distributed Online Learning with Sublinear Communication Complexity](https://mlsanity.com/paper/2103.11102/) (2021)
- [Safe Online Convex Optimization with Unknown Linear Safety Constraints](https://mlsanity.com/paper/2111.07430/) (2021)
- [Byzantine-Robust Distributed Online Learning: Taming Adversarial Participants in An Adversarial Environment](https://mlsanity.com/paper/2307.07980/) (2023)
- [Online Caching with Optimistic Learning](https://mlsanity.com/paper/2202.10590/) (2022)
- [Online Convex Optimization with Continuous Switching Constraint](https://mlsanity.com/paper/2103.11370/) (2021)
- [Lazy Lagrangians with Predictions for Online Learning](https://mlsanity.com/paper/2201.02890/) (2022)
- [Online Caching with no Regret: Optimistic Learning via Recommendations](https://mlsanity.com/paper/2204.09345/) (2022)
- [Distributed Online Private Learning of Convex Nondecomposable Objectives](https://mlsanity.com/paper/2206.07944/) (2022)
- [Dynamic Regret Analysis of Safe Distributed Online Optimization for Convex and Non-convex Problems](https://mlsanity.com/paper/2302.12320/) (2023)
- [Monotone Individual Fairness](https://mlsanity.com/paper/2403.06812/) (2024)
- [Delay-Tolerant Constrained OCO with Application to Network Resource Allocation](https://mlsanity.com/paper/2105.04005/) (2021)
- [Distributed Online Non-convex Optimization with Composite Regret](https://mlsanity.com/paper/2209.10105/) (2022)
- [Online Learning with Unknown Constraints](https://mlsanity.com/paper/2403.04033/) (2024)
- [Constrained Online Convex Optimization without Slater's Condition](https://mlsanity.com/paper/2606.31480/) (2026)
- [Gradient and Projection Free Distributed Online Min-Max Resource Optimization](https://mlsanity.com/paper/2112.03896/) (2021)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Optimized Gradient Tracking for Decentralized Online Learning](https://mlsanity.com/paper/2306.06375/) (2023)
- [Distributed Online Convex Optimization with Nonseparable Costs and Constraints](https://mlsanity.com/paper/2602.10452/) (2026)
- [Penalised FTRL With Time-Varying Constraints](https://mlsanity.com/paper/2204.02197/) (2022)
- [Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization](https://mlsanity.com/paper/2205.09571/) (2022)
- [Online Non-convex Optimization with Long-term Non-convex Constraints](https://mlsanity.com/paper/2311.02426/) (2023)
- [Safe Online Convex Optimization with Multi-Point Feedback](https://mlsanity.com/paper/2407.11471/) (2024)
- [Distributed Online Bandit Nonconvex Optimization with One-Point Residual Feedback via Dynamic Regret](https://mlsanity.com/paper/2409.15680/) (2024)
- [Optimistic Learning for Communication Networks](https://mlsanity.com/paper/2504.03499/) (2025)

## Abstract (arXiv)

This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror descent algorithm is proposed to solve this problem, where the local cost, regularization, and constraint functions are held privately and revealed only after each time slot. Without assuming Slater's condition, we first derive regret and constraint violation bounds for the algorithm and show how they depend on the stepsize sequences, the accumulated dynamic variation of the comparator sequence, the number of agents, and the network connectivity. As a result, under some natural decreasing stepsize sequences, we prove that the algorithm achieves sublinear dynamic regret and constraint violation if the accumulated dynamic variation of the optimal sequence also grows sublinearly. We also prove that the algorithm achieves sublinear static regret and constraint violation under mild conditions. Assuming Slater's condition, we show that the algorithm achieves smaller bounds on the constraint violation. In addition, smaller bounds on the static regret are achieved when the objective function is strongly convex. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.