Neural Network Models in Combinatorial Optimization

Sample Complexity Bounds for Recurrent Neural Networks with Application to Combinatorial Graph Problems

“…Here we confirm that 2 See our supplementary materials for a detailed overview on the topic. We also refer to Smith (1999); Syed & Pardalos (2013) for extensive overviews on the use of neural network models for combinatorial problems. state-of-the-art neural networks can yield a satisfactory performance with a considerably smaller number of training samples.…”

“…The intuition is that neural networks identify a mapping between pairs of graphs and solutions that generalizes to unseen input, thereby achieving a generalizable approximation to the true solution. We refer to Smith (1999); Syed & Pardalos (2013) for extensive overviews on the use of neural network models for combinatorial problems. The resulting solver promises an efficient computation scheme for combinatorial problems with clear benefits: it requires only a fixed evaluation cost when being applied to unseen data, and obtains solution schemes, even when any form of heuristic is unknown.…”

“…Neural networks for combinatorial optimization. Extensive research has applied neural networks to tasks from (combinatorial) optimization; see the overviews in (Smith, 1999;Syed & Pardalos, 2013), including various tasks (e. g., transportation and scheduling (Gupta et al, 2000)) and ranging from simple feed-forward networks to differential neural computers (Graves et al, 2016). However, the previous works rely purely on numerical demonstration and thus lack a rigorous theoretical understanding of the underlying estimation.…”