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

Yiyang Lu, Mohammad Pedramfar, Vaneet Aggarwal

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.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=7zTWz9MrLI

Changes Since Last Submission: prepared the final version based on the review comments.

Assigned Action Editor: ~Baoxiang_Wang1

Submission Number: 5436