Go to TMLR homepageDecentralized 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.
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: 1. Introduction section has been revised to reflect comments by the previous reviewers, reducing repetition and focusing on detailed examples to making our motivation clearer.
2. The Summary Table has been revised to include projection-based method for comparison, and description has been expanded to make table easier to read and understand.
3. We added literature review of Decentralized Online Convex Optimization to make our Related Works section more complete.
4. To clear confusion revolving around query oracles, we have revised the structure of our paper. In the revised version, Section 4 is for general upper-linearizable functions, while Section 5 focuses on application to specific up-concave subclasses across different feedback. This way, we use the linearizable query oracle (a wrapper for query oracle for upper-linearizable class) for Algorithm 1, and the (standard) query oracles for the extension algorithms. we also improves writing in Alg. 3 (line 7&8), Alg. 4 (line 9), and Alg. 5 (line 9), so that we clear any confusion regarding the queries.
5. To reduce confusion about notations between Problem Formulation and our proposed algorithm, DROCULO, we have adopted different notations for point of query, point of action, and local variables that the agents store and update.
6. We have revised our contribution summary to reflect these changes, and shorten the summary to three bullet points for ease of readability.
Assigned Action Editor: ~Baoxiang_Wang1
Submission Number: 5436
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