Heavy-Head Sampling for Fast Imitation Learning of Machine Learning Based Combinatorial Auction Solver

The winner determination problem of a combinatorial auction can be modeled as mixed-integer linear programming, and is a popular benchmark to evaluate modern solvers. Recent advancements in combinatorial optimization improve the branch-and-bound solving process by replacing the time-consuming heuristics with machine learning models. In this paper, by taking advantage of the heavy-head maximum depth distribution of the branch-and-bound solution trees, a heavy-head sampling strategy is proposed for the imitation learning on the combinatorial auction problems. Experimental results show that, under the small-dataset fast-training scheme and using the heavy-head sampling strategy, the final evaluation results of the trained policy on the combinatorial auction problems are improved significantly (in the sense of statistical testing), compared to using the uniform sampling strategy in previous studies.