Combinatorial optimization (CO) is fundamental to several realworld applications, from logistics and scheduling to hardware design and resource allocation.Deep reinforcement learning (RL) has recently shown significant benefits in solving CO problems, reducing reliance on domain expertise and improving computational efficiency.However, the absence of a unified benchmarking framework leads to inconsistent evaluations, limits reproducibility, and increases engineering overhead, raising barriers to adoption for new researchers.To address these challenges, we introduce RL4CO, a unified and extensive benchmark with in-depth library coverage of 27 CO problem environments and 23 state-of-the-art baselines.Built on efficient software libraries and best practices in implementation, RL4CO features modularized implementation and flexible configurations of diverse environments, policy architectures, RL algorithms, and utilities with extensive documentation.RL4CO helps researchers build on existing successes while exploring and developing their own designs, facilitating the entire research process by decoupling science from heavy engineering.We finally provide extensive benchmark studies to inspire new insights and future work.RL4CO has already attracted numerous researchers in the community and is open-sourced at https://github.com/ai4co/rl4co 1 .

Learning graphical causal models from observational data can effectively elucidate the underlying causal mechanism behind the variables. In the context of limited datasets, modelers often incorporate prior knowledge, which is assumed to be correct, as a penalty in single-objective optimization. However, this approach struggles to adapt complex and uncertain priors effectively. This paper introduces UpCM, which tackles the issue from a multi-objective optimization perspective. Instead of focusing exclusively on the DAG as the optimization goal, UpCM methodically evaluate the effect of uncertain priors on specific structures, merging data-driven and knowledge-driven objectives. Utilizing the MOEA/D framework, it achieve a balanced tradeoff between these objectives. Furthermore, since uncertain priors may introduce erroneous constraints, resulting in PDAGs lacking consistent extensions, the minimal non-consistent extension is explored. This extension, which separately incorporates positive and negative constraints, aims to approximate the true causality of the PDAGs. Experimental results demonstrate that UpCM achieves significant structural accuracy improvements compared to baseline methods. It reduces the SHD by 7.94%, 13.23%, and 12.8% relative to PC stable, GES, and MAHC, respectively, when incorporating uncertain priors. In downstream inference tasks, UpCM outperforms domain-expert knowledge graphs, owing to its ability to learn explainable causal relationships that balance data-driven evidence with prior knowledge

Pre-training GNNs to extract transferable knowledge and apply it to downstream tasks has become the de facto standard of graph representation learning. Recent works focused on designing self-supervised pre-training tasks to extract useful and universal transferable knowledge from large-scale unlabeled data. However, they have to face an inevitable question: traditional pre-training strategies that aim at extracting useful information about pre-training tasks, may not extract all useful information about the downstream task. In this paper, we reexamine the pre-training process within traditional pre-training and fine-tuning frameworks from the perspective of Information Bottleneck (IB) and confirm that the forgetting phenomenon in pre-training phase may cause detrimental effects on downstream tasks. Therefore, we propose a novelDelayedBottleneckingPre-training (DBP) framework which maintains as much as possible mutual information between latent representations and training data during pre-training phase by suppressing the compression operation and delays the compression operation to fine-tuning phase to make sure the compression can be guided with labeled fine-tuning data and downstream tasks. To achieve this, we design two information control objectives that can be directly optimized and further integrate them into the actual model design. Extensive experiments on both chemistry and biology domains demonstrate the effectiveness of DBP.

Vehicle routing problems (VRP) are very important in many realworld applications and has been studied for several decades.Recently, neural combinatorial optimization (NCO) has attracted growing research effort.NCO is to train a neural network model to solve an optimization problem in question.However, existing NCO methods often build a different model for each routing problem, which significantly hinders their application in some areas where there are many different VRP variants to solve.In this work, we make a first attempt to tackle the crucial challenge of cross-problem generalization in NCO.We formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition.In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner.In our experiments, the neural model is trained on five VRP variants and its performance is tested on eleven VRP variants.The experimental results show that the model demonstrates superior performance on these eleven VRP variants, reducing the average gap to around 5% from over 20% and achieving a notable performance boost on both benchmark datasets and real-world logistics scenarios.

Most current data is multivariable, exploring and identifying valuable information in these datasets has far-reaching impacts. In particular, discovering meaningful hidden association patterns in multivariate plays an important role. Plenty of measures for multivariate association have been proposed, yet it is still an open research challenge for effectively capturing association patterns among three or more variables, especially the scenario without any prior knowledge about those relationships. To do so, we desire a distribution-free, association type-independent and non-parametrical measure. For practical applications, such a measure should comparable, interpretable,scalable, intuitive, reliability, and robust. However, no exiting measures fulfill all of these desiderata. In this paper, taking advantage of the neighborhood information of a sample, we propose MNA, a maximal neighborhood multivariate association measure that satisfies all the above criteria. Extensive experiments on synthetic and real data show it outperforms state-of-the-art multivariate association measures.