Online Submodular Maximization via Online Convex Optimization
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910289388109824 |
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| author | Salem, Tareq Si Özcan, Gözde Nikolaou, Iasonas Terzi, Evimaria Ioannidis, Stratis |
| author_facet | Salem, Tareq Si Özcan, Gözde Nikolaou, Iasonas Terzi, Evimaria Ioannidis, Stratis |
| contents | We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, weighted threshold potential functions, reduces to online convex optimization (OCO). This is precisely because functions in this class admit a concave relaxation; as a result, OCO policies, coupled with an appropriate rounding scheme, can be used to achieve sublinear regret in the combinatorial setting. We show that our reduction extends to many different versions of the online learning problem, including the dynamic regret, bandit, and optimistic-learning settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04339 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Online Submodular Maximization via Online Convex Optimization Salem, Tareq Si Özcan, Gözde Nikolaou, Iasonas Terzi, Evimaria Ioannidis, Stratis Machine Learning Artificial Intelligence Optimization and Control We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, weighted threshold potential functions, reduces to online convex optimization (OCO). This is precisely because functions in this class admit a concave relaxation; as a result, OCO policies, coupled with an appropriate rounding scheme, can be used to achieve sublinear regret in the combinatorial setting. We show that our reduction extends to many different versions of the online learning problem, including the dynamic regret, bandit, and optimistic-learning settings. |
| title | Online Submodular Maximization via Online Convex Optimization |
| topic | Machine Learning Artificial Intelligence Optimization and Control |
| url | https://arxiv.org/abs/2309.04339 |