Distributed Online Convex Optimization with Nonseparable Costs and Constraints
It addresses a key limitation in distributed online control for network systems by handling nonseparability, which is incremental but improves efficiency for applications like multi-agent coordination.
The paper tackles distributed online convex optimization with nonseparable costs and constraints, proposing a belief consensus algorithm that achieves sublinear regret and cumulative constraint violation bounds of O(T^{1/2}), breaking the previous O(T^{3/4}) barrier and matching the lower bound.
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 stratify 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.