Adaptive Combinatorial Maximization: Approximation Guarantees Beyond Greedy Policies

This work provides new approximation guarantees for adaptive combinatorial maximization that subsume and strengthen previous results. It introduces a new policy parameter, the maximal gain ratio, which is less restrictive than the greedy approximation ratio and can lead to stronger guarantees. The guarantees support non-greedy policies, nearly adaptive submodular utility functions, and both maximization under a cardinality constraint and minimum cost coverage objectives.