Unsupervised combinatorial optimization under complex conditions: Principled objectives and incremental greedy derandomization

Fanchen Bu, Hyeonsoo Jo, Sungsoo Ahn, Kijung Shin

Keywords: Unsupervised combinatorial optimization, the probabilistic method, derandomization

TL;DR: We propose a method for probabilistic unsupervised combinatorial optimization with (1) a principled probabilistic objective construction scheme, and (2) a fast and effective derandomization scheme.

Abstract:

Combinatorial optimization (CO) has significant theoretical and practical implications.
CO problems are naturally discrete, making typical machine-learning techniques based on differentiable optimization inapplicable.
Karalias & Loukas (2020) adapted the probabilistic method, an important tool in combinatorics, to incorporate CO problems into differentiable optimization.
Their work ignited the research on unsupervised learning for CO, composed of two main components: probabilistic objectives and derandomization.
Several desirable properties of probabilistic objectives have been proposed, but without principled schemes to satisfy them.
Also, the derandomization process is still underexplored.
Motivated by the limitations, we propose our method UCom2, consisting of two schemes:
(1) a *principled* probabilistic objective construction scheme that provably satisfies the good properties, and
(2) a *fast* and *effective* derandomization scheme with a quality guarantee.
We apply UCom2 to various *complex conditions* (e.g., cardinality constraints, non-binary decisions) and problems involving them, highlighting that UCom2 is *general* and *practical*.
We further show the empirical superiority of UCom2 w.r.t. both optimization quality and speed.

Primary Area: general machine learning (i.e., none of the above)

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Submission Number: 1650