Rethinking and Benchmarking Predict-then-Optimize Paradigm for Combinatorial Optimization Problems

Numerous web applications rely on solving combinatorial optimization problems, such as energy cost-aware scheduling, budget allocation on web advertising, and graph matching on social networks. However, many optimization problems involve unknown coefficients, and improper predictions of these factors may lead to inferior decisions which may cause energy wastage, inefficient resource allocation, inappropriate matching in social networks, etc. Such a research topic is referred to as "Predict-Then-Optimize (PTO)" which considers the performance of prediction and decision-making in a unified system. A noteworthy recent development is the end-to-end methods by directly optimizing the ultimate decision quality which claims to yield better results in contrast to the traditional two-stage approach. However, the evaluation benchmarks in this field are fragmented and the effectiveness of various models in different scenarios remains unclear, hindering the comprehensive assessment and fast deployment of these methods. To address these issues, we provide a comprehensive categorization of current approaches and integrate existing experimental scenarios to establish a unified benchmark, elucidating the circumstances under which end-to-end training yields improvements, as well as the contexts in which it performs ineffectively. We also introduce a new dataset for the industrial combinatorial advertising problem for inclusive finance to open-source. We hope the rethinking and benchmarking of PTO could facilitate more convenient evaluation and deployment, and inspire further improvements both in the academy and industry within this field.

GMTR: Graph Matching Transformers

Vision transformers (ViTs) have recently been used for visual matching beyond object detection and segmentation. However, the original grid dividing strategy of ViTs neglects the spatial information of the keypoints, limiting the sensitivity to local information. Therefore, we propose \textbf{QueryTrans} (Query Transformer), which adopts a cross-attention module and keypoints-based center crop strategy for better spatial information extraction. We further integrate the graph attention module and devise a transformer-based graph matching approach \textbf{GMTR} (Graph Matching TRansformers) whereby the combinatorial nature of GM is addressed by a graph transformer neural GM solver. On standard GM benchmarks, GMTR shows competitive performance against the SOTA frameworks. Specifically, on Pascal VOC, GMTR achieves $\mathbf{83.6\%}$ accuracy, $\mathbf{0.9\%}$ higher than the SOTA framework. On Spair-71k, GMTR shows great potential and outperforms most of the previous works. Meanwhile, on Pascal VOC, QueryTrans improves the accuracy of NGMv2 from $80.1\%$ to $\mathbf{83.3\%}$, and BBGM from $79.0\%$ to $\mathbf{84.5\%}$. On Spair-71k, QueryTrans improves NGMv2 from $80.6\%$ to $\mathbf{82.5\%}$, and BBGM from $82.1\%$ to $\mathbf{83.9\%}$. Source code will be made publicly available.

Rethinking Cross-Domain Sequential Recommendation under Open-World Assumptions

Cross-Domain Sequential Recommendation (CDSR) methods aim to tackle the data sparsity and cold-start problems present in Single-Domain Sequential Recommendation (SDSR). Existing CDSR works design their elaborate structures relying on overlapping users to propagate the cross-domain information. However, current CDSR methods make closed-world assumptions, assuming fully overlapping users across multiple domains and that the data distribution remains unchanged from the training environment to the test environment. As a result, these methods typically result in lower performance on online real-world platforms due to the data distribution shifts. To address these challenges under open-world assumptions, we design an \textbf{A}daptive \textbf{M}ulti-\textbf{I}nterest \textbf{D}ebiasing framework for cross-domain sequential recommendation (\textbf{AMID}), which consists of a multi-interest information module (\textbf{MIM}) and a doubly robust estimator (\textbf{DRE}). Our framework is adaptive for open-world environments and can improve the model of most off-the-shelf single-domain sequential backbone models for CDSR. Our MIM establishes interest groups that consider both overlapping and non-overlapping users, allowing us to effectively explore user intent and explicit interest. To alleviate biases across multiple domains, we developed the DRE for the CDSR methods. We also provide a theoretical analysis that demonstrates the superiority of our proposed estimator in terms of bias and tail bound, compared to the IPS estimator used in previous work.

Mind Your Solver! On Adversarial Attack and Defense for Combinatorial Optimization

Combinatorial optimization (CO) is a long-standing challenging task not only in its inherent complexity (e.g. NP-hard) but also the possible sensitivity to input conditions. In this paper, we take an initiative on developing the mechanisms for adversarial attack and defense towards combinatorial optimization solvers, whereby the solver is treated as a black-box function and the original problem's underlying graph structure (which is often available and associated with the problem instance, e.g. DAG, TSP) is attacked under a given budget. In particular, we present a simple yet effective defense strategy to modify the graph structure to increase the robustness of solvers, which shows its universal effectiveness across tasks and solvers.

A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the solution quality. Currently, machine learning for combinatorial optimization (MLCO) has become a trending research topic, but most existing MLCO methods treat CO as a single-level optimization by directly learning the end-to-end solutions, which are hard to scale up and mostly limited by the capacity of ML models given the high complexity of CO. In this paper, we propose a hybrid approach to combine the best of the two worlds, in which a bi-level framework is developed with an upper-level learning method to optimize the graph (e.g. add, delete or modify edges in a graph), fused with a lower-level heuristic algorithm solving on the optimized graph. Such a bi-level approach simplifies the learning on the original hard CO and can effectively mitigate the demand for model capacity. The experiments and results on several popular CO problems like Directed Acyclic Graph scheduling, Graph Edit Distance and Hamiltonian Cycle Problem show its effectiveness over manually designed heuristics and single-level learning methods.

Deep Reinforcement Learning of Graph Matching

Graph matching under node and pairwise constraints has been a building block in areas from combinatorial optimization, machine learning to computer vision, for effective structural representation and association. We present a reinforcement learning solver that seeks the node correspondence between two graphs, whereby the node embedding model on the association graph is learned to sequentially find the node-to-node matching. Our method differs from the previous deep graph matching model in the sense that they are focused on the front-end feature and affinity function learning while our method aims to learn the backend decision making given the affinity objective function whatever obtained by learning or not. Such an objective function maximization setting naturally fits with the reinforcement learning mechanism, of which the learning procedure is label-free. Besides, the model is not restricted to a fixed number of nodes for matching. These features make it more suitable for practical usage. Extensive experimental results on both synthetic datasets, natural images, and QAPLIB showcase the superior performance regarding both matching accuracy and efficiency. To our best knowledge, this is the first deep reinforcement learning solver for graph matching.

Combinatorial Learning of Graph Edit Distance via Dynamic Embedding

Graph Edit Distance (GED) is a popular similarity measurement for pairwise graphs and it also refers to the recovery of the edit path from the source graph to the target graph. Traditional A* algorithm suffers scalability issues due to its exhaustive nature, whose search heuristics heavily rely on human prior knowledge. This paper presents a hybrid approach by combing the interpretability of traditional search-based techniques for producing the edit path, as well as the efficiency and adaptivity of deep embedding models to achieve a cost-effective GED solver. Inspired by dynamic programming, node-level embedding is designated in a dynamic reuse fashion and suboptimal branches are encouraged to be pruned. To this end, our method can be readily integrated into A* procedure in a dynamic fashion, as well as significantly reduce the computational burden with a learned heuristic. Experimental results on different graph datasets show that our approach can remarkably ease the search process of A* without sacrificing much accuracy. To our best knowledge, this work is also the first deep learning-based GED method for recovering the edit path.

Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching

Graph matching involves combinatorial optimization based on edge-to-edge affinity matrix, which can be generally formulated as Lawler's Quadratic Assignment Problem (QAP). This paper presents a QAP network directly learning with the affinity matrix (equivalently the association graph) whereby the matching problem is translated into a vertex classification task. The association graph is learned by an embedding network for vertex classification, followed by Sinkhorn normalization and a cross-entropy loss for end-to-end learning. We further improve the embedding model on association graph by introducing Sinkhorn based constraint, and dummy nodes to deal with outliers. To our best knowledge, this is the first network to directly learn with the general Lawler's QAP. In contrast, state-of-the-art deep matching methods focus on the learning of node and edge features in two graphs respectively. We also show how to extend our network to hypergraph matching, and matching of multiple graphs. Experimental results on both synthetic graphs and real-world images show our method outperforms. For pure QAP tasks on synthetic data and QAPLIB, our method can surpass spectral matching and RRWM, especially on challenging problems.

InstaBoost: Boosting Instance Segmentation via Probability Map Guided Copy-Pasting

Instance segmentation requires a large number of training samples to achieve satisfactory performance and benefits from proper data augmentation. To enlarge the training set and increase the diversity, previous methods have investigated using data annotation from other domain (e.g. bbox, point) in a weakly supervised mechanism. In this paper, we present a simple, efficient and effective method to augment the training set using the existing instance mask annotations. Exploiting the pixel redundancy of the background, we are able to improve the performance of Mask R-CNN for 1.7 mAP on COCO dataset and 3.3 mAP on Pascal VOC dataset by simply introducing random jittering to objects. Furthermore, we propose a location probability map based approach to explore the feasible locations that objects can be placed based on local appearance similarity. With the guidance of such map, we boost the performance of R101-Mask R-CNN on instance segmentation from 35.7 mAP to 37.9 mAP without modifying the backbone or network structure. Our method is simple to implement and does not increase the computational complexity. It can be integrated into the training pipeline of any instance segmentation model without affecting the training and inference efficiency. Our code and models have been released at https://github.com/GothicAi/InstaBoost

Learning Combinatorial Embedding Networks for Deep Graph Matching

Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of the node-wise and structure-wise affinity across graphs and the resulting objective, to guide the matching procedure effectively finding the true matching against noises. To this end, this paper devises an end-to-end differentiable deep network pipeline to learn the affinity for graph matching. It involves a supervised permutation loss regarding with node correspondence to capture the combinatorial nature for graph matching. Meanwhile deep graph embedding models are adopted to parameterize both intra-graph and cross-graph affinity functions, instead of the traditional shallow and simple parametric forms e.g. a Gaussian kernel. The embedding can also effectively capture the higher-order structure beyond second-order edges. The permutation loss model is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network allows for varying numbers of nodes in graphs for training and inference. Moreover, our network is class-agnostic with some generalization capability across different categories. All these features are welcomed for real-world applications. Experiments show its superiority against state-of-the-art graph matching learning methods.