Dec-BFTRL: Squre-Root Regret for Decentralized Online Upper-Linearizable Optimization under Separation Access with Application to Continuous Submodular Maximization

Abstract:We study decentralized online optimization of upper-linearizable payoffs over an action set under efficient separation access, with applications to online continuous diminishing-return (DR) submodular maximization. We propose Decentralized Barrier Follow-the-Regularized-Leader (Dec-BFTRL), and evaluate each agent's played action against the average of all local objectives. Each agent maps an internal iterate to a feasible action through an approximate gauge projection, communicates only a cumulative surrogate-gradient dual state, and invokes the local HybridNewton procedure to approximately minimize its post-communication BFTRL potential. For every agent, we achieve expected network-aggregate regret of $\widetilde O(\sqrt{T})$. Over $T$ rounds, each agent uses $T$ neighbor-mixing steps and $\widetilde O(T)$ separation-oracle calls. We give four wrapper instantiations covering three DR-submodular maximization problems.

Optimization and Control (math.OC); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2608.30271 [math.OC]

(or arXiv:2608.30271v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2608.30271 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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