Continuous Tensor Relaxation for Finding Diverse Solutions in Combinatorial Optimization Problems

Finding the best solution is the most common objective in combinatorial optimization (CO) problems. However, a single solution may not be suitable in practical scenarios, as the objective functions and constraints are only approximations of original real-world situations. To tackle this, finding (i) "heterogeneous solutions", diverse solutions with distinct characteristics, and (ii) "penalty-diversified solutions", variations in constraint severity, are natural directions. This strategy provides the flexibility to select a suitable solution during post-processing. However, discovering these diverse solutions is more challenging than identifying a single solution. To overcome this challenge, this study introduces Continual Tensor Relaxation Annealing (CTRA) for unsupervised-learning-based CO solvers. CTRA addresses various problems simultaneously by extending the continual relaxation approach, which transforms discrete decision variables into continual tensors. This method finds heterogeneous and penalty-diversified solutions through mutual interactions, where the choice of one solution affects the other choices. Numerical experiments show that CTRA enables UL-based solvers to find heterogeneous and penalty-diversified solutions much faster than existing UL-based solvers. Moreover, these experiments reveal that CTRA enhances the exploration ability.

Rule Mining for Correcting Classification Models

Machine learning models need to be continually updated or corrected to ensure that the prediction accuracy remains consistently high. In this study, we consider scenarios where developers should be careful to change the prediction results by the model correction, such as when the model is part of a complex system or software. In such scenarios, the developers want to control the specification of the corrections. To achieve this, the developers need to understand which subpopulations of the inputs get inaccurate predictions by the model. Therefore, we propose correction rule mining to acquire a comprehensive list of rules that describe inaccurate subpopulations and how to correct them. We also develop an efficient correction rule mining algorithm that is a combination of frequent itemset mining and a unique pruning technique for correction rules. We observed that the proposed algorithm found various rules which help to collect data insufficiently learned, directly correct model outputs, and analyze concept drift.