This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative algorithm. However, we observed that directly applying LD often leads to limited exploration. To overcome this limitation, we propose the Regularized Langevin Dynamics (RLD), which enforces an expected distance between the sampled and current solutions, effectively avoiding local minima. We develop two CO solvers on top of RLD, one based on simulated annealing (SA) and the other one based on neural network (NN). Empirical results on three classical CO problems demonstrate that both of our methods can achieve comparable or better performance against the previous state-of-the-art (SOTA) SA and NN-based solvers. In particular, our SA algorithm reduces the running time of the previous SOTA SA method by up to 80\%, while achieving equal or superior performance. In summary, RLD offers a promising framework for enhancing both traditional heuristics and NN models to solve CO problems.

Mixed Integer Linear Program (MILP) solvers are mostly built upon a Branch-and-Bound (B\&B) algorithm, where the efficiency of traditional solvers heavily depends on hand-crafted heuristics for branching. The past few years have witnessed the increasing popularity of data-driven approaches to automatically learn these heuristics. However, the success of these methods is highly dependent on the availability of high-quality demonstrations, which requires either the development of near-optimal heuristics or a time-consuming sampling process. This paper averts this challenge by proposing Suboptimal-Demonstration-Guided Reinforcement Learning (SORREL) for learning to branch. SORREL selectively learns from suboptimal demonstrations based on value estimation. It utilizes suboptimal demonstrations through both offline reinforcement learning on the demonstrations generated by suboptimal heuristics and self-imitation learning on past good experiences sampled by itself. Our experiments demonstrate its advanced performance in both branching quality and training efficiency over previous methods for various MILPs.

Augmenting the multi-step reasoning abilities of Large Language Models (LLMs) has been a persistent challenge. Recently, verification has shown promise in improving solution consistency by evaluating generated outputs. However, current verification approaches suffer from sampling inefficiencies, requiring a large number of samples to achieve satisfactory performance. Additionally, training an effective verifier often depends on extensive process supervision, which is costly to acquire. In this paper, we address these limitations by introducing a novel verification method based on Twisted Sequential Monte Carlo (TSMC). TSMC sequentially refines its sampling effort to focus exploration on promising candidates, resulting in more efficient generation of high-quality solutions. We apply TSMC to LLMs by estimating the expected future rewards at partial solutions. This approach results in a more straightforward training target that eliminates the need for step-wise human annotations. We empirically demonstrate the advantages of our method across multiple math benchmarks, and also validate our theoretical analysis of both our approach and existing verification methods.

Contrastive learning is an effective unsupervised method in graph representation learning, and the key component of contrastive learning lies in the construction of positive and negative samples. Previous methods usually utilize the proximity of nodes in the graph as the principle. Recently, the data-augmentation-based contrastive learning method has advanced to show great power in the visual domain, and some works extended this method from images to graphs. However, unlike the data augmentation on images, the data augmentation on graphs is far less intuitive and much harder to provide high-quality contrastive samples, which leaves much space for improvement. In this work, by introducing an adversarial graph view for data augmentation, we propose a simple but effective method, Adversarial Graph Contrastive Learning (ARIEL), to extract informative contrastive samples within reasonable constraints. We develop a new technique called information regularization for stable training and use subgraph sampling for scalability. We generalize our method from node-level contrastive learning to the graph level by treating each graph instance as a super-node. ARIEL consistently outperforms the current graph contrastive learning methods for both node-level and graph-level classification tasks on real-world datasets. We further demonstrate that ARIEL is more robust in the face of adversarial attacks.

Contrastive learning is an effective unsupervised method in graph representation learning. Recently, the data augmentation based contrastive learning method has been extended from images to graphs. However, most prior works are directly adapted from the models designed for images. Unlike the data augmentation on images, the data augmentation on graphs is far less intuitive and much harder to provide high-quality contrastive samples, which are the key to the performance of contrastive learning models. This leaves much space for improvement over the existing graph contrastive learning frameworks. In this work, by introducing an adversarial graph view and an information regularizer, we propose a simple but effective method, Adversarial Graph Contrastive Learning (ARIEL), to extract informative contrastive samples within a reasonable constraint. It consistently outperforms the current graph contrastive learning methods in the node classification task over various real-world datasets and further improves the robustness of graph contrastive learning. The code is at https://github.com/Shengyu-Feng/ARIEL.

The advances in deep learning have enabled machine learning methods to outperform human beings in various areas, but it remains a great challenge for a well-trained model to quickly adapt to a new task. One promising solution to realize this goal is through meta-learning, also known as learning to learn, which has achieved promising results in few-shot learning. However, current approaches are still enormously different from human beings' learning process, especially in the ability to extract structural and transferable knowledge. This drawback makes current meta-learning frameworks non-interpretable and hard to extend to more complex tasks. We tackle this problem by introducing concept discovery to the few-shot learning problem, where we achieve more effective adaptation by meta-learning the structure among the data features, leading to a composite representation of the data. Our proposed method Concept-Based Model-Agnostic Meta-Learning (COMAML) has been shown to achieve consistent improvements in the structured data for both synthesized datasets and real-world datasets.