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Using machine learning to solve combinatorial optimization (CO) problems ischallenging, especially when the data is unlabeled. This work proposes anunsupervised learning framework for CO problems. Our framework follows astandard relaxation-plus-rounding approach and adopts neural networks toparameterize the relaxed solutions so that simple back-propagation can trainthe model end-to-end. Our key contribution is the observation that if therelaxed objective satisfies entry-wise concavity, a low optimization lossguarantees the quality of the final integral solutions. This observationsignificantly broadens the applicability of the previous framework inspired byErdos' probabilistic method. In particular, this observation can guide thedesign of objective models in applications where the objectives are not givenexplicitly while requiring being modeled in prior. We evaluate our framework bysolving a synthetic graph optimization problem, and two real-world applicationsincluding resource allocation in circuit design and approximate computing. Ourframework largely outperforms the baselines based on na\"{i}ve relaxation,reinforcement learning, and Gumbel-softmax tricks.

Unsupervised Learning for Combinatorial Optimization with Principled Objective Relaxation