arXiv research

Surveying machine learning for solving graph optimization problems.

End-to-end trainable graph matching using improved combinatorial solvers.

Graph neural networks improve combinatorial optimization by leveraging inductive bias.

Bayesian Optimization for graph node subset functions.

Linear-time graph optimization using reinforcement learning.

This work proposes an unsupervised neural network framework for solving combinatorial optimization problems on graphs.

Combinatorial approach to $α$-Ricci and Lin-Lu-Yau Ricci curvatures on graphs

This paper focuses on Bayesian Optimization (BO) for objectives on combinatorial search spaces, including ordinal and categorical variables. Despite the abundance of potential applications of Combinatorial BO, including chipset configuration search and neural architecture search, only a handful of methods have been pro…

A method learns to solve multilevel combinatorial problems with two players.

This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative t…

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We prove that certain decompositions lead to a theoretically optimal condition number.…

Improves scalability of Bayesian optimization for combinatorial spaces.

Graph neural networks improve solving linear optimization problems.

Extends graph factor system to quasi-median graphs.

Survey of graph learning methods for combinatorial optimization problems.

This paper extends combinatorial semi-bandits to graph feedback, improving regret bounds.

Let a $A$ be the 1-skeleton of a triangulated topological annulus. We establish bounds on the combinatorial modulus of a refinement $A'$, formed by attaching new vertices and edges to $A$, that depend only on the refinement and not on the structure of $A$ itself. This immediately applies to showing that a disk triangul…

Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient he…

MIP-GNN uses graph neural networks to predict variable biases for MIP solvers.

The paper finds minimum Steklov eigenvalues on combinatorial graphs.

This paper proposes a new method to learn combinatorial patterns for airline crew pairing optimization.

Neural networks struggle with TSP beyond small instances, requiring new approaches.

New algorithm eliminates arms to minimize regret in complex bandit problems.

The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the algorithms instead? In many real-world applications, it is typically the case t…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for …

New method improves combinatorial optimization by capturing dependencies among solution variables.

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs…

New combinatorial type helps distinguish plane curve topologies.

We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links…

GFlowNets improve combinatorial optimization by efficiently sampling from solution spaces.

Extends knot concordance invariant to balanced spatial graphs using grid homology.

A fast ML method solves complex combinatorial auction problems.

Proposes a new optimization method for local graph clustering.

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solution…

BPNNs learn to solve combinatorial problems faster and more accurately.

In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input, which captures relationships between nodes. Furthermore, to approximate solutions to…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity…

New method learns DAGs from data without acyclicity constraint.

The paper extends log-Sobolev inequalities to matrix-valued settings using combinatorial methods.

A gradient-based method learns the structure of TAN for Bayesian network classifiers.

We prove that the total curvature of any planar graph with nonnegative combinatorial curvature is an integral multiple of $\frac{1}{12}.$ As a corollary, this answers a question proposed by T. Réti.

Neural model with parameterized algorithms improves graph CO problem solving.

Optimizes matching in weighted graphs with semi-bandit sampling.

A new deep learning framework for topological data.

Introduces a new manifold from a graph subgraph.

Develops a combinatorial semi-bandit method for electric vehicle charging station selection.

Graph machine learning lacks a balanced theory, focusing on expressive power and optimization.

Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve bec…