  Combinatorial optimization (CO) is naturally discrete, making machine
learning based on differentiable optimization inapplicable. Karalias & Loukas
(2020) adapted the probabilistic method to incorporate CO into differentiable
optimization. Their work ignited the research on unsupervised learning for CO,
composed of two main components: probabilistic objectives and derandomization.
However, each component confronts unique challenges. First, deriving objectives
under various conditions (e.g., cardinality constraints and minimum) is
nontrivial. Second, the derandomization process is underexplored, and the
existing derandomization methods are either random sampling or naive rounding.
In this work, we aim to tackle prevalent (i.e., commonly involved) conditions
in unsupervised CO. First, we concretize the targets for objective construction
and derandomization with theoretical justification. Then, for various
conditions commonly involved in different CO problems, we derive nontrivial
objectives and derandomization to meet the targets. Finally, we apply the
derivations to various CO problems. Via extensive experiments on synthetic and
real-world graphs, we validate the correctness of our derivations and show our
empirical superiority w.r.t. both optimization quality and speed.
