  The success of machine learning solutions for reasoning about discrete
structures has brought attention to its adoption within combinatorial
optimization algorithms. Such approaches generally rely on supervised learning
by leveraging datasets of the combinatorial structures of interest drawn from
some distribution of problem instances. Reinforcement learning has also been
employed to find such structures. In this paper, we propose a radically
different approach in that no data is required for training the neural networks
that produce the solution. In particular, we reduce the combinatorial
optimization problem to a neural network and employ a dataless training scheme
to refine the parameters of the network such that those parameters yield the
structure of interest. We consider the combinatorial optimization problems of
finding maximum independent sets and maximum cliques in a graph. In principle,
since these problems belong to the NP-hard complexity class, our proposed
approach can be used to solve any other NP-hard problem. Additionally, we
propose a universal graph reduction procedure to handle large scale graphs. The
reduction exploits community detection for graph partitioning and is applicable
to any graph type and/or density. Experimental evaluation on both synthetic
graphs and real-world benchmarks demonstrates that our method performs on par
with or outperforms state-of-the-art heuristic, reinforcement learning, and
machine learning based methods without requiring any data.
