Decentralized Projection-free Online Upper-Linearizable Optimization with Applications to DR-Submodular Optimization

Abstract:We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the flexibility of upper-linearizable function frameworks, effectively generalizing traditional DR-submodular function optimization. We obtain the regret of $O(T^{1-\theta/2})$ with communication complexity of $O(T^{\theta})$ and number of linear optimization oracle calls of $O(T^{2\theta})$ for decentralized upper-linearizable function optimization, for any $0\le \theta \le 1$. This approach allows for the first results for monotone up-concave optimization with general convex constraints and non-monotone up-concave optimization with general convex constraints. Further, the above results for first order feedback are extended to zeroth order, semi-bandit, and bandit feedback.

Optimization and Control (math.OC); Computational Complexity (cs.CC); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2501.18183 [math.OC]

(or arXiv:2501.18183v3 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2501.18183 Focus to learn more arXiv-issued DOI via DataCite

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