Improve the competitive ratio without comparable complexity

Improve the competitive ratio for the monotone submodular matroid secretary problem on arbitrary matroids using an approach that does not introduce complexity comparable to that of Multilevel Dynamic Thinning.

Background

The paper obtains an 8.699-competitive algorithm for the monotone submodular matroid secretary problem on arbitrary matroids by combining a learning phase, frozen marginal weights, and Dynamic Thinning. Replacing Dynamic Thinning with Multilevel Dynamic Thinning yields a slightly better factor of approximately 8.6, but the paper notes that this modification substantially increases both analytical and implementation complexity.

The unresolved question is whether a different method can improve the competitive ratio beyond the reported guarantees while avoiding a comparable increase in complexity.