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arXiv · 2501.18183

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

Yiyang Lu·Mohammad Pedramfar·Vaneet Aggarwal
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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.

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Yiyang Lu, Mohammad Pedramfar, Vaneet Aggarwal. 2025-01-30. Decentralized Projection-free Online Upper-Linearizable Optimization with Applications to DR-Submodular Optimization. https://arxiv.org/abs/2501.18183

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