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

2025-06-20

AI Summary

This paper identifies an inherent misalignment in unsupervised combinatorial optimization (UCO): during training, models optimize continuous probabilistic solutions and differentiable losses, whereas testing relies on non-differentiable derandomization to obtain deterministic solutions—causing training loss reduction to not necessarily improve actual performance. We are the first to systematically formulate and empirically validate this misalignment across diverse combinatorial optimization tasks. To mitigate it, we integrate differentiable derandomization into the end-to-end training pipeline, enabling consistent optimization of both probabilistic solution modeling and deterministic solution generation. Experiments demonstrate that our approach significantly improves the correlation between training objectives and test performance, establishing a new design paradigm for UCO. Concurrently, we uncover novel challenges introduced by differentiable derandomization—particularly gradient instability—thereby motivating further investigation into robust training strategies for unsupervised discrete optimization.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Misalignment between training and testing in unsupervised combinatorial optimization
• Lower training losses do not ensure better post-derandomization performance
• Challenges in aligning training with differentiable derandomization

Innovation

• Unsupervised combinatorial optimization with continuous decisions
• Differentiable derandomization during training
• Improved training-test alignment via empirical exploration