Various neural network models have been proposed to tackle combinatorial
optimization problems such as the travelling salesman problem (TSP). Existing
learning-based TSP methods adopt a simple setting that the training and testing
data are independent and identically distributed. However, the existing
literature fails to solve TSP instances when training and testing data have
different distributions. Concretely, we find that different training and
testing distribution will result in more difficult TSP instances, i.e., the
solution obtained by the model has a large gap from the optimal solution. To
tackle this problem, in this work, we study learning-based TSP methods when
training and testing data have different distributions using adaptive-hardness,
i.e., how difficult a TSP instance can be for a solver. This problem is
challenging because it is non-trivial to (1) define hardness measurement
quantitatively; (2) efficiently and continuously generate sufficiently hard TSP
instances upon model training; (3) fully utilize instances with different
levels of hardness to learn a more powerful TSP solver. To solve these
challenges, we first propose a principled hardness measurement to quantify the
hardness of TSP instances. Then, we propose a hardness-adaptive generator to
generate instances with different hardness. We further propose a curriculum
learner fully utilizing these instances to train the TSP solver. Experiments
show that our hardness-adaptive generator can generate instances ten times
harder than the existing methods, and our proposed method achieves significant
improvement over state-of-the-art models in terms of the optimality gap.

本文研究了使用自适应难度方法的基于学习的旅行商问题方法，通过定义硬度测量，使用硬度自适应生成器生成不同难度的实例，再利用课程学习器完全利用这些实例来训练 TSP 求解器。实验结果表明，我们的硬度自适应生成器可以生成比现有方法更困难的实例，而我们提出的方法在最优性差距方面显著优于最先进的模型。

学会使用硬度自适应课程解决旅行商问题

Learning to Solve Travelling Salesman Problem with Hardness-adaptive Curriculum

Classic machine learning methods are built on the $i.i.d.$ assumption that
training and testing data are independent and identically distributed. However,
in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering
the sharp drop of classic machine learning algorithms' performances under
distributional shifts, which indicates the significance of investigating the
Out-of-Distribution generalization problem. Out-of-Distribution (OOD)
generalization problem addresses the challenging setting where the testing
distribution is unknown and different from the training. This paper serves as
the first effort to systematically and comprehensively discuss the OOD
generalization problem, from the definition, methodology, evaluation to the
implications and future directions. Firstly, we provide the formal definition
of the OOD generalization problem. Secondly, existing methods are categorized
into three parts based on their positions in the whole learning pipeline,
namely unsupervised representation learning, supervised model learning and
optimization, and typical methods for each category are discussed in detail. We
then demonstrate the theoretical connections of different categories, and
introduce the commonly used datasets and evaluation metrics. Finally, we
summarize the whole literature and raise some future directions for OOD
generalization problem. The summary of OOD generalization methods reviewed in
this survey can be found at this http URL

该研究论文系统而全面地讨论了 Out-of-Distribution generalization 问题，其中包括它的定义、方法论、评估以及对未来的启示和发展方向，以及包括无监督表示学习在内的现有方法。

面向外部分布泛化：一项调查

Towards Out-Of-Distribution Generalization: A Survey

Approaches based on deep neural networks have achieved striking performance
when testing data and training data share similar distribution, but can
significantly fail otherwise. Therefore, eliminating the impact of distribution
shifts between training and testing data is crucial for building
performance-promising deep models. Conventional methods assume either the known
heterogeneity of training data (e.g. domain labels) or the approximately equal
capacities of different domains. In this paper, we consider a more challenging
case where neither of the above assumptions holds. We propose to address this
problem by removing the dependencies between features via learning weights for
training samples, which helps deep models get rid of spurious correlations and,
in turn, concentrate more on the true connection between discriminative
features and labels. Extensive experiments clearly demonstrate the
effectiveness of our method on multiple distribution generalization benchmarks
compared with state-of-the-art counterparts. Through extensive experiments on
distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO,
we show the effectiveness of our method compared with state-of-the-art
counterparts.

本文主要研究基于深度神经网络的方法在训练数据与测试数据分布不一致时的性能问题，并通过学习训练样本的权重以消除特征之间的依赖关系，从而提高深度模型的性能。通过在多个分布泛化基准测试上的实验，与同类研究相比，我们的方法取得了很好的效果。