Minimum Cost Adaptive Submodular Cover

• URL: http://arxiv.org/abs/2208.08351v2
• Date: Tue, 21 May 2024 20:53:18 GMT
• Title: Minimum Cost Adaptive Submodular Cover
• Authors: Hessa Al-Thani, Yubing Cui, Viswanath Nagarajan,
• Abstract summary: We consider the problem of minimum cost cover of adaptive-submodular functions. We show that our algorithm simultaneously achieves a $(p+1)p+1cdot (ln Q+1)p$ approximation guarantee for all $pge 1$.
• Score: 4.680686256929023
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Adaptive submodularity is a fundamental concept in stochastic optimization, with numerous applications such as sensor placement, hypothesis identification and viral marketing. We consider the problem of minimum cost cover of adaptive-submodular functions, and provide a $4(1+\ln Q)$-approximation algorithm, where $Q$ is the goal value. In fact, we consider a significantly more general objective of minimizing the $p^{th}$ moment of the coverage cost, and show that our algorithm simultaneously achieves a $(p+1)^{p+1}\cdot (\ln Q+1)^p$ approximation guarantee for all $p\ge 1$. All our approximation ratios are best possible up to constant factors (assuming $P\ne NP$). Moreover, our results also extend to the setting where one wants to cover {\em multiple} adaptive-submodular functions. Finally, we evaluate the empirical performance of our algorithm on instances of hypothesis identification.

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