Adaptive Submodular Ranking and Routing
This work addresses stochastic optimization challenges in search ranking and active learning, with incremental improvements over prior special cases.
The authors tackled the problem of adaptively selecting a sequence of elements to cover random scenarios at minimum expected cost, using submodular functions, and achieved a logarithmic factor approximation algorithm that is optimal unless P=NP. They extended this to an adaptive vehicle routing problem with metric costs, nearly matching best-known bounds.
We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario is captured by an individual submodular function, where the scenario is said to be covered when its function value goes above a given threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible (unless P=NP). This problem unifies and generalizes many previously studied problems with applications in search ranking and active learning. The approximation ratio of our algorithm either matches or improves the best result known in each of these special cases. Furthermore, we extend our results to an adaptive vehicle routing problem, where costs are determined by an underlying metric. This routing problem is a significant generalization of the previously-studied adaptive traveling salesman and traveling repairman problems. Our approximation ratio nearly matches the best bound known for these special cases. Finally, we present experimental results for some applications of adaptive ranking.