Improved Approximate Regret for Decentralized Online Continuous Submodular Maximization via Reductions

• URL: http://arxiv.org/abs/2602.09502v1
• Date: Tue, 10 Feb 2026 07:59:30 GMT
• Title: Improved Approximate Regret for Decentralized Online Continuous Submodular Maximization via Reductions
• Authors: Yuanyu Wan, Yu Shen, Dingzhi Yu, Bo Xue, Mingli Song,
• Abstract summary: We show how to exploit gaps between approximate convex setting bounds and regret bounds.<n>We also show that focusing free algorithms can efficiently handle complex decision sets.<n>Our key techniques are from D-OCSM to decentralized online convex optimization (D-OCO)
• Score: 59.626542575681725
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To expand the applicability of decentralized online learning, previous studies have proposed several algorithms for decentralized online continuous submodular maximization (D-OCSM) -- a non-convex/non-concave setting with continuous DR-submodular reward functions. However, there exist large gaps between their approximate regret bounds and the regret bounds achieved in the convex setting. Moreover, if focusing on projection-free algorithms, which can efficiently handle complex decision sets, they cannot even recover the approximate regret bounds achieved in the centralized setting. In this paper, we first demonstrate that for D-OCSM over general convex decision sets, these two issues can be addressed simultaneously. Furthermore, for D-OCSM over downward-closed decision sets, we show that the second issue can be addressed while significantly alleviating the first issue. Our key techniques are two reductions from D-OCSM to decentralized online convex optimization (D-OCO), which can exploit D-OCO algorithms to improve the approximate regret of D-OCSM in these two cases, respectively.

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