doubly stochastic matrix
Differentiable Extensions with Rounding Guarantees for Combinatorial Optimization over Permutations
Continuously extending combinatorial optimization objectives is a powerful technique commonly applied to the optimization of set functions. However, few such methods exist for extending functions on permutations, despite the fact that many combinatorial optimization problems, such as the quadratic assignment problem (QAP) and the traveling salesperson problem (TSP), are inherently optimization over permutations.
Differentiable extensions with rounding guarantees for combinatorial optimization over permutations
Continuously extending combinatorial optimization objectives is a powerful technique commonly applied to the optimization of set functions. However, few such methods exist for extending functions on permutations, despite the fact that many combinatorial optimization problems, such as the quadratic assignment problem (QAP) and the traveling salesperson problem (TSP), are inherently optimization over permutations.
5938b4d054136e5d59ada6ec9c295d7a-Paper.pdf
The widely studiedGeneralized Min-Sum-Set-Cover(GMSSC) problem serves as a formal model for the setting above. GMSSC is NP-hard and the standard application ofno-regretonline learning algorithms iscomputationally inefficient, because they operate in the space of rankings. In this work, we show how to achievelowregret for GMSSC inpolynomial-time.
Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spaces
The method scales well with the number of points, and it can be used to find the global solution for large-scale problems with thousands of points.
Learning symmetries via weight-sharing with doubly stochastic tensors Putri A. van der Linden
This yields learnable kernel transformations that are jointly optimized with downstream tasks.
