Minimum Cost Adaptive Submodular Cover
This addresses stochastic optimization challenges in applications like sensor placement and hypothesis identification, offering near-optimal theoretical guarantees.
The paper tackles the problem of minimum cost cover for adaptive-submodular functions, providing a 4(1+ln Q)-approximation algorithm and extending it to minimize the p-th moment of cost with a (p+1)^{p+1}·(ln Q+1)^p approximation for all p≥1, with these ratios being best possible up to constants assuming P≠NP.
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.