Learning to solve large-scale Mixed Integer Program (MIP) problems is an emerging research topic, and policy learning-based Large Neighborhood Search (LNS) has been a popular paradigm. However, the explored space of LNS policy is often limited even in the training phase, making the learned policy sometimes wrongly fix some potentially important variables early in the search, leading to local optimum in some cases. Moreover, many methods only assume binary variables to deal with. We present a practical approach, termed Binarized-Tightening Branch-and-Search for Large Neighborhood Search (BTBS-LNS). It comprises three key techniques: 1) the ``Binarized Tightening" technique for integer variables to handle their wide range by binary encoding and bound tightening; 2) an attention-based tripartite graph to capture global correlations among variables and constraints for an MIP instance; 3) an extra branching network as a global view, to identify and optimize wrongly-fixed backdoor variables at each search step. Experiments show its superior performance over the open-source solver SCIP and LNS baselines. Moreover, it performs competitively with, and sometimes better than the commercial solver Gurobi (v9.5.0), especially on the MIPLIB2017 benchmark chosen by Hans Mittelmann, where our method can deliver 10\% better primal gaps compared with Gurobi in a 300s cut-off time.

Foundation Models (FMs) have demonstrated remarkable success in fields like computer vision and natural language processing, yet their application to combinatorial optimization remains underexplored. Optimization problems, often modeled as graphs, pose unique challenges due to their diverse structures, varying distributions, and NP-hard complexity. To address these challenges, we propose OPTFM, the first graph foundation model for general combinatorial optimization. OPTFM introduces a scalable multi-view graph transformer with hybrid self-attention and cross-attention to model large-scale heterogeneous graphs in $O(N)$ time complexity while maintaining semantic consistency throughout the attention computation. A Dual-level pre-training framework integrates node-level graph reconstruction and instance-level contrastive learning, enabling robust and adaptable representations at multiple levels. Experimental results across diverse optimization tasks show that models trained on OPTFM embeddings without fine-tuning consistently outperform task-specific approaches, establishing a new benchmark for solving combinatorial optimization problems.

Branch-and-bound (B\&B) has long been favored for tackling complex Mixed Integer Programming (MIP) problems, where the choice of branching strategy plays a pivotal role. Recently, Imitation Learning (IL)-based policies have emerged as potent alternatives to traditional rule-based approaches. However, it is nontrivial to acquire high-quality training samples, and IL often converges to suboptimal variable choices for branching, restricting the overall performance. In response to these challenges, we propose a novel hybrid online and offline reinforcement learning (RL) approach to enhance the branching policy by cost-effective training sample augmentation. In the online phase, we train an online RL agent to dynamically decide the sample generation processes, drawing from either the learning-based policy or the expert policy. The objective is to strike a balance between exploration and exploitation of the sample generation process. In the offline phase, a value function is trained to fit each decision's cumulative reward and filter the samples with high cumulative returns. This dual-purpose function not only reduces training complexity but also enhances the quality of the samples. To assess the efficacy of our data augmentation mechanism, we conduct comprehensive evaluations across a range of MIP problems. The results consistently show that it excels in making superior branching decisions compared to state-of-the-art learning-based models and the open-source solver SCIP. Notably, it even often outperforms Gurobi.

Data plays a pivotal role in the development of both classic and learning-based methods for Mixed-Integer Linear Programming (MILP). However, the scarcity of data in real-world applications underscores the necessity for MILP instance generation methods. Currently, these methods primarily rely on iterating random single-constraint modifications, disregarding the underlying problem structure with constraint interrelations, thereby leading to compromised quality and solvability. In this paper, we propose ACM-MILP, a framework for MILP instance generation, to achieve adaptive constraint modification and constraint interrelation modeling. It employs an adaptive constraint selection mechanism based on probability estimation within the latent space to preserve instance characteristics. Meanwhile, it detects and groups strongly related constraints through community detection, enabling collective modifications that account for constraint dependencies. Experimental results show significant improvements in problem-solving hardness similarity under our framework. Additionally, in the downstream task, we showcase the efficacy of our generated instances for hyperparameter tuning. Source code is available: https://github.com/Thinklab-SJTU/ACM-MILP.

Machine learning (ML) has been actively adopted in Linear Programming (LP) and Mixed-Integer Linear Programming (MILP), whose potential is hindered by instance scarcity. Current synthetic instance generation methods often fall short in closely mirroring the distribution of original datasets or ensuring the feasibility and boundedness of the generated data — a critical requirement for obtaining reliable supervised labels in model training. In this paper, we present a diffusion-based LP/MILP instance generative framework called MILP-FBGen. It strikes a balance between structural similarity and novelty while maintaining feasibility/boundedness via a meticulously designed structure-preserving generation module and a feasibility/boundedness-constrained sampling module. Our method shows superiority on two fronts: 1) preservation of key properties (hardness, feasibility, and boundedness) of LP/MILP instances, and 2) enhanced performance on downstream tasks. Extensive studies show two-fold superiority that our method ensures higher distributional similarity and 100% feasibility in both easy and hard datasets, surpassing current state-of-the-art techniques.

We propose a novel multi-scale neural network for Granger causality discovery (MSNGC) in multivariate time series. Compared with existing counterparts, our model avoids the explicit data segmentation between series and between time lags for the first time. By extracting diverse causal information from the data with different delay ranges and then integrating them effectively via the learned attention weights, it can capture the complete causal relationships between all the series and provide accurate weighted adjacency matrix estimation. Thus, further interpretable inference can be better supported. Specifically, we propose a consistency-based thresholding algorithm for binary causal structure inference, an effect sign detection method to distinguish the positive causal effects from the negative ones, and a self-adaptive lag discovery algorithm to identify the lagged time points. Experiments on multiple benchmarks demonstrate that our model significantly outperforms the state-of-the-art methods.

Standard classification models rely on the assumption that all the classes of interest are equally represented in training datasets. However, visual phenomena exhibit a long-tailed distribution, such that many standard approaches fail to properly model and result in a considerable degeneration on accuracy. The recent methods have produced encouraging results, but their efforts only seek to simulate the statistical relationship between data and labels and compensate for imbalanced data-related issues, without addressing the underlying causal mechanisms. In this paper, a comprehensive structural causal model is developed to excavate the intrinsic causal mechanism between data and labels. Specifically, we assume that each input is constructed from a mix of causal factors and non-causal factors, and only the causal factors cause the classification judgments. In order to extract such causal factors from inputs and then reconstruct the invariant causal mechanisms, we propose a Causal Invariant Transformation algorithm for Long-tailed recognition (CITL), which generates diverse data to avoid the over-fitting on the tail classes and enforces the learnt representations to maintain the causal factors and eliminate the non-causal factors. Our extensive experimental results on several widely used datasets have demonstrated the effectiveness of our proposed CITL approach.

The estimation of Individual Treatment Effect (ITE) is a challenging problem in causal inference, due to the missing counterfactual data and the selection bias. In this paper, we propose a novel representation learning framework via the Learnable Query based transformer for Treatment Effect Estimation (LQTEE). A certain number of queries are learned in a sample-agnostic way and extract global critical features from covariate and treatment data separately. We also propose the hierarchical propensity score regularized adversarial loss to obtain balanced covariate representations, and the mutual orthogonal constraint to force queries to focus on diverse parts of covariates, thus the impact of instrumental variables can be adaptively reduced. Treatment representation learning enables our estimator to support general-purpose treatments, and more importantly, it can reveal the underlying patterns of data-generation process efficiently. Extensive experiments show that our ITE estimator significantly outperforms the state-of-the-art methods.