Work

Distributed Online Convex Optimization with Long-Term Constraints: No Cumulative Constraint Violation

Year: 2026

Type: article

Abstract: This paper investigates the problem of distributed online optimization with long-term constraints (LTC), where constraints are not required to be satisfied at each time step but only over a longer horizon. We first propose a baseline algorithm based on online regularized Lagrangian functions, achieving a regret bound of O(T3/4). By refining the Lagrangian functions and optimization strategies, we further improve the regret bound to O(T2/3). Notably, our results enforce strict satisfaction of LTC over time, in contrast to most existing works that focus solely on achieving sublinear cumulative constraint violations. Moreover, the obtained performance matches the optimal guarantees achievable in the centralized setting. Finally, we demonstrate the effectiveness of our approach through a distributed online regularized linear regression problem.

Source: International Journal of Network Dynamics and Intelligence

DOI: 10.53941/ijndi.2026.100006

Authors: Difeng Zhang, Shaofu Yang

Institution: Southeast University

Language: English

Topic: Advanced Bandit Algorithms Research

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: diamond

Funders: Alexander von Humboldt-Stiftung, National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G6273817310, G6665774762, G7738687920