Stronger Approximation Guarantees for Non-Monotone γ-Weakly DR-Submodular Maximization

• URL: http://arxiv.org/abs/2601.00611v1
• Date: Fri, 02 Jan 2026 08:44:10 GMT
• Title: Stronger Approximation Guarantees for Non-Monotone γ-Weakly DR-Submodular Maximization
• Authors: Hareshkumar Jadav, Ranveer Singh, Vaneet Aggarwal,
• Abstract summary: We study a non-monotone $$-weakly DR-submodular function over a down-closed convex body.<n>Our approach combines a Frank-Wolfe-guided continuous machine learning framework with a $$-greedy step.<n>This results in state-of-the-art guarantees for non-monotone $$-weakly DR-submodular over down-closed convex bodies.
• Score: 42.50444156527582
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone $γ$-weakly DR-submodular function over a down-closed convex body. Our main result is an approximation algorithm whose guarantee depends smoothly on $γ$; in particular, when $γ=1$ (the DR-submodular case) our bound recovers the $0.401$ approximation factor, while for $γ<1$ the guarantee degrades gracefully and, it improves upon previously reported bounds for $γ$-weakly DR-submodular maximization under the same constraints. Our approach combines a Frank-Wolfe-guided continuous-greedy framework with a $γ$-aware double-greedy step, yielding a simple yet effective procedure for handling non-monotonicity. This results in state-of-the-art guarantees for non-monotone $γ$-weakly DR-submodular maximization over down-closed convex bodies.

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