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Combinatorial Optimisation problems arise in several application domains andare often formulated in terms of graphs. Many of these problems are NP-hard,but exact solutions are not always needed. Several heuristics have beendeveloped to provide near-optimal solutions; however, they do not typicallyscale well with the size of the graph. We propose a low-complexity approach foridentifying a (possibly much smaller) subgraph of the original graph where theheuristics can be run in reasonable time and with a high likelihood of findinga global near-optimal solution. The core component of our approach is LeNSE, areinforcement learning algorithm that learns how to navigate the space ofpossible subgraphs using an Euclidean subgraph embedding as its map. To solveCO problems, LeNSE is provided with a discriminative embedding trained usingany existing heuristics using only on a small portion of the original graph.When tested on three problems (vertex cover, max-cut and influencemaximisation) using real graphs with up to $10$ million edges, LeNSE identifiessmall subgraphs yielding solutions comparable to those found by running theheuristics on the entire graph, but at a fraction of the total run time.

LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation