On Training-Test (Mis)alignment in Unsupervised Combinatorial Optimization: Observation, Empirical Exploration, and Analysis

TL;DR

This paper investigates the mismatch between training and testing phases in unsupervised combinatorial optimization, proposing a differentiable derandomization approach to improve alignment and analyzing its challenges.

Contribution

It introduces a differentiable derandomization method for better training-test alignment in UCO and provides empirical insights into its benefits and challenges.

Findings

Differentiable derandomization improves training-test alignment.

Lower training loss does not always lead to better test performance.

Challenges arise when integrating differentiable derandomization into training.

Abstract

In unsupervised combinatorial optimization (UCO), during training, one aims to have continuous decisions that are promising in a probabilistic sense for each training instance, which enables end-to-end training on initially discrete and non-differentiable problems. At the test time, for each test instance, starting from continuous decisions, derandomization is typically applied to obtain the final deterministic decisions. Researchers have developed more and more powerful test-time derandomization schemes to enhance the empirical performance and the theoretical guarantee of UCO methods. However, we notice a misalignment between training and testing in the existing UCO methods. Consequently, lower training losses do not necessarily entail better post-derandomization performance, even for the training instances without any data distribution shift. Empirically, we indeed observe such undesirable cases. We explore a preliminary idea to better align training and testing in UCO by including a differentiable version of derandomization into training. Our empirical exploration shows that such an idea indeed improves training-test alignment, but also introduces nontrivial challenges into training.