Rethinking Branching on Exact Combinatorial Optimization Solver: The First Deep Symbolic Discovery Framework
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Keywords: Combinatorial Optimization, Branch and Bound, Deep Symbolic Optimization, Learn to Optimize, Machine Learning for Combinatorial Optimization
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TL;DR: In this submission, we develop the first deep symbolic discovery framework to learn high-performance branching policies for lightweight and reliable application to exact combinatorial optimization solvers.
Abstract: Machine learning (ML) has been shown to successfully accelerate solving NP-hard combinatorial optimization (CO) problems under the branch and bound framework.
However, the high training and inference cost and limited interpretability of ML approaches severely limit their wide application to modern exact CO solvers. In contrast, human-designed policies---though widely integrated in modern CO solvers due to their compactness and reliability---can not capture data-driven patterns for higher performance. To combine the advantages of the two paradigms, we propose the first symbolic discovery framework---namely, deep symbolic discovery for exact combinatorial optimization solver (Symb4CO)---to learn high-performance symbolic policies on the branching task. Specifically, we show the potential existence of small symbolic policies empirically, employ a large neural network to search in the high-dimensional discrete space, and compile the learned symbolic policies directly for fast deployment. Experiments show that the Symb4CO learned purely CPU-based policies consistently achieve *comparable* performance to previous GPU-based state-of-the-art approaches.
Furthermore, the appealing features of Symb4CO include its high training (*ten training instances*) and inference (*one CPU core*) efficiency and good interpretability (*one-line expressions*), making it simple and reliable for deployment. The results show encouraging potential for the *wide* deployment of ML to modern CO solvers.
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Primary Area: general machine learning (i.e., none of the above)
Submission Number: 5144
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