Author

A. Kuhnle

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Preprint Oct 2026

Stronger Hardness for Submodular Maximization Subject to a Matroid Constraint

Maximizing a submodular function subject to a matroid constraint is a cornerstone problem in combinatorial optimization. The state-of-the-art algorithm for this problem obtains $0.401$-approximation~\cite{buchbinder2024constrained}, and the state-of-the-art hardness result shows that no polynomial time algorithm can ob...

Moran Feldman, A. Kuhnle · 0 citations

#machine learning Preprint Oct 2026

How Inefficient Is Natural Gradient Descent? From Exact Optimality to \Theta ( \sqrt{ \log d } ) Divergence

Natural gradient descent (NGD) underlies common methods in ML. For dually flat families, idealized NGD on the forward Kullback--Leibler objective follows the mixture geodesic which is often longer than the shortest Fisher--Rao path. We quantify this overhead by the inefficiency ratio $R \ge 1$, the Fisher length of t...

Guni Sharon, A. Kuhnle · 0 citations

Preprint Sep 2026

Submodular Welfare under Routing Coupling: A Hierarchical Decomposition with Perturbation Guarantees

This paper studies joint submodular welfare maximization and routing over graphs, where agents select items under diminishing returns and transport them through a network with congestion-dependent costs. Although welfare maximization admits matroid-based approximations and routing reduces to shortest paths under modula...

Joan Vendrell Gallart, Nhat-Minh Tang-Nguyen, A. Kuhnle et al. · 0 citations