Distributed Online Convex Optimization with Nonseparable Costs and Constraints

• URL: http://arxiv.org/abs/2602.10452v2
• Date: Tue, 17 Feb 2026 15:43:25 GMT
• Title: Distributed Online Convex Optimization with Nonseparable Costs and Constraints
• Authors: Zhaoye Pan, Haozhe Lei, Fan Zuo, Zilin Bian, Tao Li,
• Abstract summary: We study a group of agents, networked via a communication graph, that collectively select actions to minimize a sequence of nonseparable global cost functions.<n>We propose a distributed online primal-dual belief consensus algorithm, where each agent maintains and updates a local belief of the global collective decisions.
• Score: 7.671875264854638
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper studies distributed online convex optimization with time-varying coupled constraints, motivated by distributed online control in network systems. Most prior work assumes a separability condition: the global objective and coupled constraint functions are sums of local costs and individual constraints. In contrast, we study a group of agents, networked via a communication graph, that collectively select actions to minimize a sequence of nonseparable global cost functions and to satisfy nonseparable long-term constraints based on full-information feedback and intra-agent communication. We propose a distributed online primal-dual belief consensus algorithm, where each agent maintains and updates a local belief of the global collective decisions, which are repeatedly exchanged with neighboring agents. Unlike the previous consensus primal-dual algorithms under separability that ask agents to only communicate their local decisions, our belief-sharing protocol eliminates coupling between the primal consensus disagreement and the dual constraint violation, yielding sublinear regret and cumulative constraint violation (CCV) bounds, both in $O({T}^{1/2})$, where $T$ denotes the time horizon. Such a result breaks the long-standing $O(T^{3/4})$ barrier for CCV and matches the lower bound of online constrained convex optimization, indicating the online learning efficiency at the cost of communication overhead.

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