# On Distributed Online Convex Optimization with Sublinear Dynamic Regret and Fit

arXiv: https://arxiv.org/abs/2001.03166 · HTML: https://mlsanity.com/paper/2001.03166/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2020.

## Built on by (most cited first, 7 of 7)

- [Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization](https://mlsanity.com/paper/2105.00321/) (2021)
- [Simultaneously Achieving Sublinear Regret and Constraint Violations for Online Convex Optimization with Time-varying Constraints](https://mlsanity.com/paper/2111.07707/) (2021)
- [Dynamic Regret Analysis of Safe Distributed Online Optimization for Convex and Non-convex Problems](https://mlsanity.com/paper/2302.12320/) (2023)
- [QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM](https://mlsanity.com/paper/2208.02777/) (2022)
- [Distributed Online Non-convex Optimization with Composite Regret](https://mlsanity.com/paper/2209.10105/) (2022)
- [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)

## Abstract (arXiv)

In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex functions. The objective and constraint functions are revealed locally to the nodes, at each time, after taking an action. Naturally, the constraints cannot be instantaneously satisfied. Therefore, we reformulate the problem to satisfy these constraints in the long term. To this end, we propose a distributed primal-dual mirror descent based approach, in which the primal and dual updates are carried out locally at all the nodes. This is followed by sharing and mixing of the primal variables by the local nodes via communication with the immediate neighbors. To quantify the performance of the proposed algorithm, we utilize the challenging, but more realistic metrics of dynamic regret and fit. Dynamic regret measures the cumulative loss incurred by the algorithm, compared to the best dynamic strategy. On the other hand, fit measures the long term cumulative constraint violations. Without assuming the restrictive Slater's conditions, we show that the proposed algorithm achieves sublinear regret and fit under mild, commonly used assumptions.