Unified Projection-Free Algorithms for Adversarial DR-Submodular Optimization

• URL: http://arxiv.org/abs/2403.10063v2
• Date: Fri, 26 Apr 2024 21:05:00 GMT
• Title: Unified Projection-Free Algorithms for Adversarial DR-Submodular Optimization
• Authors: Mohammad Pedramfar, Yididiya Y. Nadew, Christopher J. Quinn, Vaneet Aggarwal,
• Abstract summary: This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial DR-submodular optimization. For every problem considered in the non-monotone setting, the proposed algorithms are either the first with proven sub-linear $alpha$-regret bounds or have better $alpha$-regret bounds than the state of the art.
• Score: 28.598226670015315
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions, different constraints, and types of stochastic queries. For every problem considered in the non-monotone setting, the proposed algorithms are either the first with proven sub-linear $\alpha$-regret bounds or have better $\alpha$-regret bounds than the state of the art, where $\alpha$ is a corresponding approximation bound in the offline setting. In the monotone setting, the proposed approach gives state-of-the-art sub-linear $\alpha$-regret bounds among projection-free algorithms in 7 of the 8 considered cases while matching the result of the remaining case. Additionally, this paper addresses semi-bandit and bandit feedback for adversarial DR-submodular optimization, advancing the understanding of this optimization area.

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