# Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps

arXiv: https://arxiv.org/abs/2508.09411 · HTML: https://mlsanity.com/paper/2508.09411/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Structure-Dependent Regret and Constraint Violation Bounds for Online Convex Optimization with Time-Varying Constraints](https://mlsanity.com/paper/2603.14319/) (2026)

## Abstract (arXiv)

This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively minimize the global loss function. To this end, under no-Euclidean distance metrics, we propose a distributed online stochastic mirror descent convex-concave optimization algorithm with time-varying predictive mappings. Taking dynamic saddle point regret as a performance metric, it is proved that the proposed algorithm achieves the regret upper-bound in O(max Tθ1, Tθ2 (1+VT ) ) for the general convex-concave loss function, where θ1, θ2 ∈(0,1) are the tuning parameters, T is the total iteration time, and VT is the path-variation. Surely, this algorithm guarantees the sublinear convergence, provided that VT is sublinear. Moreover, aiming to achieve better convergence, we further investigate a variant of this algorithm by employing the multiple consensus technique. The obtained results show that the appropriate setting can effectively tighten the regret bound to a certain extent. Finally, the efficacy of the proposed algorithms is validated and compared through the simulation example of a target tracking problem.